Regarding eclectic ethics, you are right that in America today many and maybe most would not consciously trace their morals to Christianity. But few behaviors contradicting the Christian ethics are viewed as ethical (much more are practiced as an ethical weakness, e.g. various transgressions from the Christian marital code of ethics). Historically, the cultural makeup of today's Americans has been shaped almost exclusively by Protestant ethics of the First and Second Spiritual Awakenings, that gave America its Revolution and its Civil War. If religion were not pushed from the public view by the secularist minority, we'd have more recognition of the Christian roots of common ethics.
Rand, however, is outside of the pale of Christian ethics, primarily because of the issue of kindness that we've been discussing. So I'd say that while an American who is unaware of Rand may be equally unaware of historical Christianity, his ethics are of Christian roots; and an American sympathetic to Rand's ethical teaching would have to reconcile the traditional ethics with Rand's and would come up with an eclectic system.
Altruism, has all the above simple problems that kindness has, with an added feature of having a much wider range of social and political implications. For example, the advocacy of altruistic ethics, when manifested politically, become the moral justifications for forcing altruistic behavior on others. The entire notion of altruism, is that an individual must put his own interests into the service of others, without personal benefit. Using morality as a basis of political conformity is totalitarianism at its worse.
I say their is no such thing as altruism. That the individual is incapable of both setting aside their own self interests, as well as accurately determining the best interest of others so as to accurately rearrange his own self interest. Furthermore, even if both impossibilities were to occur, the outcome would be same as the individual's self interest to start with by definition, as any change that occurred was an intended part of that self interest and thereby it could not have been set aside to start with. Altruism is therefore a hoax. It does not exist. There never has been a true altruist. But the political results of its deceptions have been, and still are, very real.
Ethics, directly traceable back to ancient Greece, has been a developing discipline, throughout history, as has been Christian ethics. Ethics as an area of study was pretty much buried during the roller coaster era of Christian rule, its development took off again with the protestant reformation and loss of Christian power and authority. With ethics once again being allowed to be developed separate from Christianity, it took off independent of and in conjunction with the dominate Christian religion. Trade back and forth, between the various forms of Christian and secular ethics, had influence both ways. Introduction of its Asian forms as well as reintroduction of its ancient Odinistic forms added to the general mix, as ethics over all became increasingly secular again.
Christian ethics, even by the leaders of the reformation, was substantially different from what we today call Christian ethics. From Martin Luther's support of the mass slaughters in the peasant revolts through the Divine Right of Kings and on to the divine right of governments, very little of Christian ethics then had anything in common with today's Christian ethics, that can't also be traced back to developments that came out of pre- Christian ancient Greece and Rome.
Now I'm not saying that their was no major Christian developments, in spite of its influence. There were many like Calvin who had a tremendous influence on the work ethic, even after it was largely compromised. But over all, ethics from the end of the 17th century, has been primarily reestablished and developed as a secular discipline. I say it has influenced Christianity every bit as much, if not more, than Christianity has influenced it. This is particularly true with regard to the early 18th century developments in ethics, which so heavily influenced our American Revolution and the founders of our country. Christian ethics of that time taught that government authority came from God and did not allow for any of it to occur.
As for today, Christian ethics is a mixed bag. The secular attack on its conservative side is absolutely mind boggling. The secularists ability to influence so many with such obvious propaganda, that anyone can see through for what it is, is only made possible by the failure of Christians at taking hard ethical stands, and thereby are either viewed as being hypocritical or wanting to establish a theocracy. And so we end up with knee jerk politics from both sides.
Now as far as Rand being outside the pale of Christian ethics goes, so also is almost everyone else. Some of Rand's comments on kindness, as I think I recall them, are still quite novel. Being such, they are going to fall out side any existing mainstream positions, Christian, secular, or otherwise. How much of it was pure attention grabbing so as to present her theory regarding selfishness, we will never know. But one thing is for certain, refined and compromised versions of several significant concepts in ethics, are today easier to explain than they were before Rand.