I always try to find the context when people are outraged by a quote, so I started by trying to figure out what the definition is of the quoted "capitalist democracy". Wikipedia gave "page does not exist", so I went to google. Google gave me a bunch of news article about Peter Thiel pamphlet. The term don't seems to exist outside it.
So I went back to the pamphlet and looked if it defined the term only to find that the above quote is the first time he uses "capitalist democracy". The only thing that then make sense is to look above in the text to see what if anything related to either capitalist or democracy. However the only thing he say is that "capitalism simply is not that popular", and "I no longer believe that freedom and democracy are compatible".
So I can only really make a blind guess what he is trying to say. In 1920 9% of women were working, while about 90-95% of men were working. It might be this difference that the pamphlet is referring to, but if so, it is also missing the historical context of that date. World War 1 ended in 1918, and during that year the US congress had planned to issue a female war draft because they ran out of men to fuel the war machine and the voluntary female work places did not attract enough women. Naturally you can't force people into the military without rightfully open up the issue of voting rights. The draft, and associated discussion regarding voting was more or less decided, but then the war ended. The female draft became first delayed and then scrapped. The question of voting as we all know did however get voted in.
It is in the context of those first few years after world war 1 that the pamphlet bring up that quote. It seems to have no insight to 1920 economical environment, and even less so with the economy of 2009, that its hard to figure out what the intended meaning is supposed to be. Maybe the whole pamphlet was written to say that women should not vote because 1920s enjoyed political optimism?, but that too would also just be an other guess to what would be a very odd thing to write.