This sounds pretty small-"l" libertarian to me:
'Has nothing whatsoever to do with bedroom behavior. Its the public in your face and down our kids throats behavior that is intolerable. Keep it off our public squares, out of our playgrounds, out of our parks, out of our public restrooms, off our streets, out of our schools, out of our churches, off of our TV, out of our movies, out of our judiciary, out of our military, out of our government and out of our faces!! Take it back to your private bedrooms. Thankyouverymuch!!'
- Jim Robinson, 05/26/2011
In the New Testament, Rom 1:26ff: For this cause God gave them up unto vile affections: for even their women did change the natural use into that which is against nature: And likewise also the men, leaving the natural use of the woman, burned in their lust one toward another; men with men working that which is unseemly, and receiving in themselves that recompence of their error which was meet.
Paul discusses numerous other sins but then concludes in verse 32, Who knowing the judgment of God, that they which commit such things are worthy of death, not only do the same, but have pleasure in them that do them.
I don't know what Paul had in mind in verse 32 re "worthy of death." I think the consensus might be that he was referring to the second death, viz. eternal damnation. Regardless, he was saying that homosexuality is an abomination in public or private.
I also don't understand your reference to small vs large case libertarian. I don't think it's relevant. Libertarians universally demand/espouse that which God condemns, and that's enough for me.