Their platonic ideal would support women’s and queer liberation, personally oppose racism (but would support every individual’s right to be bigoted). They’d be in favor of the right to use drugs. They’d oppose religious power. They’d believe minorities and women should arm ourselves.

That is where you are dead wrong. I read libertarian/ancap subreddits now and then, and they are very used to these statements. Their answer is truthful: they support freedom, not progressivism. In other words, they opposed to the authority of a central state. They don’t care if individuals or private organizations want exclude certain people. They very much think that excluding certain races, women or LGBT from their shops or organizations is a libertarian virtue. More so, many libertarians are extremely traditionalist, religious people who want the state to go away so they are free to form communities base their own insane ideas.