Actual quote:

The 1920s were the last decade in American history during which one could be genuinely optimistic about politics. 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.[1]

As we can see, especially if we read the whole article and grasp the context, Thiel is not arguing that women voting per se is bad. He is arguing that the consequences of woman suffrage and other changes since 1920s were summarily bad, because it led to increase of government intervention.

Imagine somebody saying "last redistricting led to Trump supporters now having majority in my state's Senate, this is awful" - do you think he argues against Trump voters having voting rights or against concept of electoral districts? He is unhappy with the outcome, not the process that led to it.

Thus, it is clear that what Thiel objects is removal of freedoms and not giving it to somebody who is "not like him".

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

Part of the reason I've mostly checked out of political discussion is because it's so partisan. I flat out don't believe half the things people claim Trump said. In most cases either the quote is cherry picked or the context is flat out misconstrued.

I've lost count of how many times I've seen outrage at something Hilary or Trump said or wrote, only to conclude what was said was reasonable and the outrage was manufactured for and by stupid people.