Answer: They all had their impetus and in many cases their origin in moral convictions arising directly from evangelical Christianity and the Bible.
Granted, non-believers also supported them; the moral convictions upon which they were founded were, after all, accessible to reason as well as to those who believe in biblical revelation. But they ought to be enough to make the case that there are few things more American, more historically obvious, more constitutional, or more- in the best sense of the word- liberal than the concept that even ideas whose origin is explicitly religious and even sectarian ought to have access to the public square. The oft-repeated fear of theocracy expressed by the secularist Left ignores the rather obvious point that in a diverse and even minimally democratic society a narrowly sectarian political agenda based solely on sectarian belief has no possible chance of prevailing. Until and unless America becomes a great deal more culturally and religiously homogeneous than it is, ideas having their origin in religious conviction will only have even the faintest chance of prevailing if they can appeal to those outside the religious tradition(s) in which they originate on the basis of pure reason, accessible to believer and non-believer alike.
Curiously, then-Senator Barack Obama gave what I consider one of the finest analyses of the role of religious conviction in the making of public policy back in 2006. While I didn't agree with everything he said- I respond to it here- it quite eloquently drew the line between arguing for a public policy because "God says so" and arguing for that same policy because God says so and because it makes sense, for good secular reasons. But the Democratic party and even the president himself seem to be drawing back from that argument. They prefer to speak of "freedom of worship" rather than "freedom of religion;" the notion seems to be that religious convictions per se are best contained within the walls of a church, and should not be allowed to influence people's political behavior.
There is a biblical word for a castrated faith like that. It's called "unbelief." One cannot be a disciple of Jesus- indeed, an honest follower of any religion- while keeping it confined to one's private life. Genuine faith influences every aspect of one's existence. Jesus wasn't exactly big on "part-time discipleship;" no honest man or woman could be.
There's also a secular word for it, which Jesus was also known to use on occasion. It's "hypocrisy."
Oh. And one other thing.
Yes, we can, we must and we do legislate morality. It seems not to occur to the cultural left that the Thirteenth Amendment, for example, legislates morality. So do the laws against, say, murder and rape. Or would the position that "I personally think that it's wrong to own other people, but I wouldn't want to impose my beliefs on anyone else" be a morally admissible one? To kill someone who displeases me in cold blood? To force sexual contact against an unwilling partner? And if not, how can it be morally coherent to say that one personally believes abortion to be murder, but that it should nevertheless be legal?
The narrative of the secularist Left is an odd one that assumes that the First Amendment's prohibition against "the establishment of religion, or (the) prohibiting (of) free exercise thereof" was somehow an attempt to contain religion's influence on public policy. It wasn't. Quite to the contrary, its purpose was precisely to protect the individual conscience not only in the integrity of its private exercise, but the opportunity to advocate its conclusions in the public square not only as an option for individual belief, but as the basis for public action. And every descendent of a slave has good reason to be grateful for that fact.