As I understand it, that's some Jerry Falwell, Pat Robertson shit.

Back in the 70s liberal/liberalism meant pretty much the same thing in the U.S. as elsewhere. Nixon even called his reelection something along the lines of "a victory for western liberal democracy." Part of liberalism is a focus on rights of the individual, including civil rights. Civil rights and many other liberation movements of the era used the language of that aspect of liberalism.

Enter a bunch of religious assholes of the time. They loved all the pull-yourself-up-by-your-bootstraps, right to private property, greed, etc. of individual rights but had a big problem with women wearing pants and expecting to be able to go to work without being sexually assaulted, gay people existing openly and breathing, and probably the civil rights movement too but it was going out of style to be open about that. They started using liberal/liberalism in a denigrating way to describe feminists, LGBT people, and any other group that got their puritanical knickers in a twist.

After a couple decades the terms were completely divorced from their original political theory definitions which would, I think, have Republicans considered more liberal than Democrats. But I suppose that could depend on which aspects of liberalism you give more weight to.