He didn't say the "US majority," though, he said "women."

So, what place do women have in his ideal, libertarian state?

I think that's a relevant question.

For example, presuming women are disinclined to vote for libertarians, how do you reconcile the "democracy" in "capitalist democracy" and "universal suffrage?" Is he saying if we have universal suffrage then we have to pick one: capitalism or democracy?

That seems to be the implication of his statement.