No they dont. They get bent out of shape about fascists who want to push their perverted morality on everyone in public including our children.
I would like to have some libertarian explain to me any aspect of social conservatism that is anti-liberty.
I'll quote Wikipedia:
Liberty is the concept of ideological and political philosophy that identifies the condition to which an individual has the right to behave according to one's own personal responsibility and free will.
"Anti-liberty," therefore, would be the antithesis of the above.
Many social conservatives would dance in the streets on the day when homosexuality was re-criminalized, thereby denying, by law, homosexuals the right to behave according to their own personal responsibility and free will. Ergo, you have your one aspect of social conservatism that is anti-liberty.
You tossed up the softball, Einstein. Don't blame me because you didn't quite think that brilliant line of argument through.