I think it's unlikely. Going from "chivalrous man" to "womanizer" seems a bit of a stretch.
It appears that it most commonly just means 'feminist' based on what I observe in the majority of the search results I find in 少納言, a balanced corpus. The corpus doesn't seem to include many quotes from young people, though - the youngest in these results is someone born in the 1970s. On the other hand, the quotes themselves are not exactly old - the time span is 1988-2008.
The other usages are present, too, but I think they are secondary.
Interestingly, the quote below suggests that the "chivalrous man" usage was already considered wrong decades ago.
「フェミニスト」イコール「女に優しい軟弱な男」イコール「女に優しい軟弱な男」、という常識的な誤りさえ知っていたかどうか怪しい -- 松本侑子『私の本棚』（1993）
I would say the secondary usages of フェミニスト for "chivalrous man" and "feminazi" are less representative or at least context-dependent. Also, internet usage does not necessarily represent how people write and talk elsewhere. フェミ might be pejorative but that's not too different from how "libs" might be used pejoratively more often than "liberals".