"Interestingly, the eldest neoconservatives began not on the right but on the left."
That is indeed the origin of the term. But it is only true of a certain portion, and the school of thought later called by that label has antecedents older that these "eldest" ones, of whom it isn't true.
The Trotskey connection is misdiagnosed. Allegiance to Trotskey rather than Stalin was a secular intellectual's way of opposing the Soviet Union. This goes back as far as the 30s and 40s, initally to experiences in the Spanish civil war and to the Moscow trials. It was admitted that Russia was a tyranny and unsupportable, but this admission was not at first allowed to take with it support for Marxism.
The reason this matters for the history of neoconservatism is that it amounted to a rehabilitation of patriotism within a sector of the hard left. These thinkers saw the liberal traditions of the US as morally valuable. They at first kept their objections to capitalism as an economic system - though gradually, the diagnosis of tyranny was generalized from Stalin's personality to communism as such. These were still recognizably intellectuals of the left, but strongly anti-communist from moral principle - Hannah Arendt and Arthur Koestler are examples. They were not neoconservatives. But they were the kind of left these "ur-neoconservatives" came from.
Politically, their natural home in the 50s and early 60s remained the right wing of the democratic party. The democratic party was still anti-communist, from Truman to John and Joe Kennedy. But the new left brought marxism into the mainstream of the democratic party. And by then this crowd had already concluded that Marxism led to tyranny, Trotskey or not.
The ascendency of the new left after 1968 presented them a dilemma, whether to stay on the left or move to the right in response. It was not a shift of allegiance from Stalin to Israel. It was continuing moral opposition to tyranny, and a growing patriotism toward the United States with it, that felt morally tainted by the "new left".
There was a connection to allegiance to Israel, but through an intellectual analysis of the causes of tyranny and the alternatives to it. In other words, it ran anti-Nazi, anti-totalitarian, pro-Israel and anti-communist - all before the Dems bought into the hard "new" left.
What happened after that and made them neo-cons was their grudging rehabilitation of capitalism. Kristol's most famous book in the 70s was "Two Cheers for Capitalism". It wasn't three cheers - he was not a traditional libertarian or old right conservative. But the welfare state did not seem to be working as advertized, the effort to build it was triggering a rise in hard left thought, and the warnings of classical liberals like Hayek about the connection between economic interventionism and socialism looked vindicated. At this time, a Daniel Patrick Monihayn was also in basically this camp. The debate played out in the pages of Commentary magazine.
Morality was worth protecting, and social policy could be destructive to it. And this meant the social conservatives were not anathema anymore, but had a point. Richard Neuhas and his "First Things" is an example of the crossover that occurred on this subject. Gertrude Himmelfarb (Kristol's wife) and her books on virtue are another example.
The neocons were also more open to the social sciences other than economics than previous conservatives had been. Their intellectual background drew heavily on sociological traditions (e.g. class analysis in Arendt). They employed the newer social sciences in debate with leftists who until then had nearly undisputed possession of those fields. From this strand came Monihayn's report on the family, Charles Murray's "Losing Ground", and the like.
What all of this amounted to was a diagnosis of soft socialism that regarded some version of it as pretty much inevitable, but feared moral and political consequences of too extreme application of socialist ideas in economics. They did not have to make their peace with the welfare state, as they came from the left. They did have to notice its problems. In doing so, they rendered significant policy service to the older right.
It was for this in particular that they were tapped by the early Reagan administration. Also for their robust cold warrior anti-communism. Reagan felt that the democratic party has left him, too, though earlier - he switched camps in the 50s, essentially under the influence of Buckley's National Review, post war consensus on the right. (Which united economic concerns of the pro-business right with the social concerns of traditionalist right, while reading both isolationists and imitators of European fascism out of the party). So he understood recent neo-con party switchers like Jeanne Kirkpatrick and Bill Bennett.
Dealing with the Reagan admininstration also meant working with the religious right, which hitherto had little to do with this crowd. Intellectually they were worlds apart. Neuhas style classical-liberal catholicism and some Jewish orthodoxy bridged some of the differences, but not all.
And there Straussianism was a factor. Strauss was essentially an atheist, but believed in the social utility of religion. Not as it is often depicted by critics, as an intrument of control, but as furthering morality and providing solace in a fundamentally bleak world. (That bkeakness was influenced in part by traditions of European existentialism). Strauss basically thought most people go at least slightly crazy about their own mortality. And some forms of that craziness are more harmful than others. The moral monotheisms are less harmful than modern forms of political extremism, which Strauss understood as modern religions.
Why did this matter? Because it meant hyper-intellectual secularists could and did make their peace with religious conservatism, valuing its social effects and fearing the alternatives, without believing its actual teachings. The intellecutal circles in which these people moved had previously been pretty relentlessly secularist, and especially hostile to "low brow", "unsophisticated" religiousity, to literalism and evangelicals. But the combination of some Neuhas, some orthodoxy, some Straussianism, tamed this, as a political matter. It was not entirely mutual, incidentally - traditional conservatives sometimes deeply distrusted this crowd on essentially religious grounds.
It is fair to say the influence of the neo-cons declined somewhat under Bush pere. The reason was essentially that Bush pere came from a social background that did not need imported intellectualism and did not particularly respect it.
An example of the difference can be seen in Baker's foreign policy attitudes, which were essentially status quo and pragmatic. He wanted to keep Yugoslavia together. He prompted Bush's "chicken kiev" speech calling for avoiding a rapid breakup of the Soviet Union as destabilizing. While the neocons wanted to spread democratic revolution and depose tyrants. The Bush pere administration stemmed intellectually from late 50s ideas, if not earlier. New England WASP noblesse oblige, public service, good stewardship, the business of America is business etc. It was easy to maneuver him into raising taxes, as the "responsible thing to do", where ideological neo-cons would never have done so.
But it is innaccurate to say they went away in the 90s. They did not. While Gingrich himself is an old style conservative, he was an unusually intellectual and ideological one, and the ideas he inhaled from the think tanks were chocked full of neocon policies. The one place his "revolution" in 1994 differed materially from the neo-con platform was in its dedication to the eventually drastic reduction of the welfare state.
That was a libertarian dream clear back to the New Deal. But neo-cons generally did not have the "third cheer" for capitalism that involves, and have made their peace with a significant welfare state. So in 1994, the neocons were marginally to the left of Gingrich's revolution.
Also in the course of the 90s, they lamented rather different things about the Clinton administration than some other conservatives. They saw a decline in the national sense of mission, with the end of the cold war and a cynical poll driven politics. Compared to the furor of the campaign against communism, the period seemed aimless.
Understand, their intellectual traditions are all about an epic crisis facing the west, in which the valiant intellectual who engages on the moral side tips the scales and allows truth and justice to triumph, where disaster threatened. So they started talking about national greatness and Teddy Roosevelt's original call to make the US a great power. The end of the cold war fit their self image only if followed by a pax Americana in which democracy would be spread across the world and morality would reign. This all tapped into a strand of US foreign policy making that Walter Russel Mead labels "Missionary" or Wilsonian.
As for the articles of the creed as presented, they are true enough but not exhaustive. On the particular subject of democracy and its tendency toward vulgarity, for instance, some of it is just moralism, some of it is intellectual elitism. Strauss spoke of the purpose of liberal education as the attempt to found an aristocracy within democratic mass society, for example. There was in this no hostility to institutional republicanism. Rather, an intellectual elitism effectively stands in for the old class obligations of a now vanished WASP establishment.
Is the underlying world view Manichean? Moralist certainly. One of the serious services Strauss performs for the intellectual right is his systematic refutation of relativism and all similar modern philosophic tendencies that obscure or deny a basis for morality. But also politically realist, comfortable with the existence and exercise of power - though wary of tyranny.
The reason I hestitate to call it "Manichean" is that it does not really involve a unified principle of evil. The religious right has such an understanding, libertarians are sure it is the state, the left tends to fix everything on capitalism, various wackier views see favorite conspiracies. This is alien to the neo-con outlook, which regards moral failing as a kind of mistake and/or lassitude to which people are always subject.
Tyranny is probably the closest thing to a principle of evil to neo-cons. But they will excuse dictatorship in hard enough circumstances, judging by results rather than the form of government (Lee Kuan Yew was not another Saddam). Gross abuse of human rights, lack of chivalry in the exercise of power, that is the principle evil. Tyranny just frequently leads to it, expands its scale, and makes it harder to stop. I don't see this as particularly "Manichean"; classical liberals felt the same way.
But it is a moralist view, a philosophically robust one that is unswayed by all of the modern schools of thought that soften or erase moral edges. It does not think of moral failings "therapeutically", or as mere symptoms of supposedly more "objective" conditions, or as subjective opinions within those who denounce immoral behavior, or as relative to a particular culture. Evil is evil and must be fought.
Evil individuals may reform - chivalry toward the defeated is part of the "code" - but evil principles deserve outright defeat. This is expected to be a perpetual process, something each generation is called on to do, not a utopian one that can be settled once and for all by the right institutions or the victory of one cause. This is "permanent struggle", yes, diagnosed as permanent due to the likely recurrance of new varities of evil principles, and accepted as such, since the risks seen in utopian bids for "final victory" as judged as a mirage. (Part of the mirage that led the 30s-40s hard left astray, in fact).
Now some particular corrections about Strauss, easily the most misunderstood component of the affair. Which is hardly surprising, since he deliberately courted being misunderstood.
He did not "teach that democracy must be internationalized to eliminate tyranny". He called the United States the bulwark of freedom in a world facing the prospect of world-wide tyranny, in the context of the cold war. That much is true. And he wrote extensively about tyranny, in particular diagnosing the motives of would be tyrants along classical rather than modern ideological lines.
To Strauss, Stalin was not first a communist and then also a tyrant, he was a tyrant one of whose means of rule was deliberately spread preposterous ideas about something called "communism". Strauss had an extra layer of hostility to modern tyranny from its effects on freedom of thought. This was essentially a redirected anti-clericalism that sees modern ideologies as new religions for which states systematically propagandize and persecute.
Traditional anti-clerical attitudes of elitist secular intellectuals are aimed by Strauss at a new target - the "group think" and inquisitorial nature of modern political thought. "PC" is a perfect target for Straussian ridicule. Straussians can live with the traditionally religious because they are generally far more sincere, moral, and open minded than the real Torquemadas of the day. (Although in the presence of truly strident and anti-intellectual literalism, the root anti-clericalism will often show itself, if only in ironic asides).
As for the fight against vulgarity, Straussian ideas on that score are openly aristocratic. Straussians are frankly elitist, without it undermining their support of institutional republicanism. Smart educated people have better taste than the masses and are more capable - though they are not necessarily any more trustworthy, indeed frequently the opposite.
Only moralizing education "guards the guardians". Responsible, moderate, and patriotic policies are duties of the educated. When they seek power cynically instead, they trash morality and open the door to tyranny. That is the form of moral evil to which they are particularly exposed, and guarding against it is the first task of liberal education.
This is far from being a cartoonish Hitlerism about how to lead the masses by the nose by inventing an enemy. It is more like a diagnosis of the problem with a self appointed Gramscian leftist "aristocracy", which is two steps away from Stalinism, and morally disarmed in the fight to prevent those steps from being taken. As such, Straussians see tyranny from an intellectual left as a live possibility, one that must be countered by a responsible, patriotic, moralistic, and self-limiting intellectual elite that refuses to side with such a left.
Historically speaking, Strauss is the antidote to Gramsci.