Taking gender out of the equation, I think the naturally tendency of all humans is to advocate for free speech when such speech tends to benefit them and people are against free speech when such speech goes against them.

Take for example all these leftists on social media that advocate for censorship. They only do so because right now the power and flow of society benefits them. If tomorrow all of a sudden National Socialists were in power and censoring leftists you would immediately see a flip where the leftists would start screaming for free speech.

There are only a few people that always advocate for free speech at all times and it's usually only because these people were once oppressed because of their speech so they understand the dangers of ever censoring speech. That would be say the founding fathers of the USA who understood the dangers of the British and Catholic Church censoring speech because it hurt them so they advocated with free speech and when they had the power to censor speech they chose instead not to censor because they had experienced first hand the problems of censorship. They then tried to instill those values in Americans and that worked for a while but now too many people living today no longer understand the issues of censoring speech. They don't fathom that one day it could be them being censored. They think they'll always be in the right because we're at the dawn of a new age of humanity or whatever. The lessons of the past have been forgotten and the people are naive.

How does this apply to women? Well, women are benefiting the most between the sexes by a significant margin. This means women will be more likely to advocate for censorship because they see less problems with it and the censorship is benefiting women far more than men. If for example our society was censoring women from insulting men, censoring feminists from suggesting women are equal to men, censoring women who speak disrespectfully to a man, or censoring groups that promoted women in the workforce, in slutdom etc... And the censorship was benefiting men over women, you would see less women advocate for censorship.

I also think there is a natural lean where holding all else constant, women prefer censorship than men. The reason for this comes down to the fact that men are stronger, smarter and more capable than women. That means men have less to fear from the free speech of others because men have more power on an individual basis to ensure the free speech of others doesn't negatively impact them. Women have less individual power than men so therefore are always more threatened by the free speech of others, most especially men. This creates a naturally lean where women always prefer censorship over free speech.

Between the two factor, we see a large descrepency between the two sexes.