I have to thank some of the comments above for causing me to look into Thiel more closely. As such, it seems you've cast what he thinks of the women's vote quite wrong. These are the two relevant quotes from an essay he wrote[1]:

> Since 1920, the vast increase in welfare beneficiaries and the extension of the franchise to women — two constituencies that are notoriously tough for libertarians — have rendered the notion of “capitalist democracy” into an oxymoron.

> It would be absurd to suggest that women’s votes will be taken away or that this would solve the political problems that vex us. While I don’t think any class of people should be disenfranchised, I have little hope that voting will make things better.

He's not saying that women shouldn't vote, but that they tend vote against his libertarian politics and thus he sees little hope for democratic solutions. Are we not allowed to think that certain politics are wrong or against our own wishes, and that groups tend to vote for certain types of politics? It seems to me to be very normal to feel a lack of hope or even apathy when looking at voting patterns.

[1] https://www.cato-unbound.org/2009/04/13/peter-thiel/educatio...