Do you buy the socialist George Lakoff's framework? He's all about framing, doncha know. If you buy into his framing, you will reach the exact conclusion he wants you to.
There are far more than two dimensions in the mapping of political ideologies.
You sir are arguing from a false premise (that the two axies' for political though are conformism and interdependence). Trying to view the world threw this lens will only give you stupid answers.
No reasoning person calls themselves 'independent' in the modern world (build you own computer out of sand?). The question is 'How do you manage the exchange of support?'. Pure authoritarians want the government to do the managing. Pure capitalists let markets work it out without government interferance beyond the effort to keep the markets functioning. Authoritarians also love to regulate morality.
It appears that, using the site's terminology, "moral liberalism" is the desire for individual control over both social and economic private matters, while "moral conservatism" is the desire for state control over social and economic matters. In that sense, "libertarianism" does seem to equal "liberalism", but the definition of "liberalism" isn't the one commonly accepted today, at least in the U.S.
For example, here is the site's definition of "ultra liberalism":
Ultra Liberalism is an extreme form of Economic Liberalism.
It is the view (sometimes called Minimal Statism, or Minarchism) that government should be as small as possible.
Ultra-liberalist usually agree that government should be restricted to its "minimal" state functions of government (courts, police, prisons, defense). Some other minarchists include in the role of government the management of essential common infrastructure (roads, money).
That definition makes me an "ultra liberal", which in any modern context is ridiculous. It aligns more with classical liberalism, which is a theory of limited (and, in the U.S., strictly Constitutional) government that these days is more accurately termed "libertarianism". But I would challenge anyone to find me someone who identifies himself as a modern liberal who would agree that "government should be restricted to its 'minimal' state functions of government (courts, police, prisons, defense)." Yes, libertarianism and liberalism are the same when liberalism is defined as the desire for as limited a government as possible, but no one these days in the U.S. defines liberalism that way.
As far as who a "liberal" (per this site; a libertarian as defined elsewhere) would vote for given either a party-line Democrat or a party-line Republican, my choice is Republican. They frequently fail the limited-government test on social matters, and occasionally on economic matters, but they are objectively more economically free-market than Democrats and they do occasionally limit government, at least in economic matters. From a limited-government perspective, the Democrats are as bad with economic matters as are the Republicans with social matters, but the Democrats also fail to seek limited-government answers to social questions - they simply tend to implement a different kind of government control than the Republicans. Thus on a whole Republicans tend to do better than Democrats on limiting the size and scope of government, although there are exceptions and the difference in some areas is becoming increasingly small.
------------- Libertarian Capitalism is an extreme form of Moral Liberalism.
Let's start here. They've jumped from libertarian theory, to economic theory. Capitalism in particular. Then economic theory is equated to moral theory. It's completely irrational. It's a pile of putrid rubbish.
"For libertarians, there are no positive rights (such as to food or shelter or health care), only negative rights (such as to not be assaulted, abused, robbed or censored).
A right belongs to the individual and no polarity whatsoever. Moral codes exist to protect those rights. You have a right to life and a right to sovereignty of will and to property. It is absolutely impossible to have a right to food, shelter and heathcare if they are not your property, or the service was not paid for in a fair exchange, because those things never belonged to you in the first place. You must obtain them. If obtaining them involves other people whatsoever, you must deal with them in a fair and just manner. The only way to deal in a fair and just manner is to ensure the rights of all parties are protected at all times.
Libertaianism is a fundamental theory of rational being interaction that protects every individual and all of their rights absolutely. Liberalism is a theory of interaction that is by it's very nature completely arbitrary and undefinable in any general, specific, or permanent basis at all. Liberalism is basically an authoritarian tyranny plain and simple. The concept of rights is arbitrary and based on whatever the powers that be dictate. Liberalism is authoritarian serfdom and slavery.
Read Hayek, The Road to Serfdom, The Constitution of Liberty, or visit some valid libertarian philosophy sources to learn about libertarianism. The Libertarian party is not a source, nor are the moronic pamphleteer sites you've sourced. Note that sometime before the middle of the last century the liberals co-opted the word liberalism. Most of the founders of this country were classical liberals, essentially libertarians. Modern liberals co-opted the word as a con to reintroduce their authoritarian socialist schemes.
As far as learning about modern liberalism, read John Rawls, A Theory of Justice. That's gives framework for all variations of liberalism.