Believing one gender more by default is as sexist as it gets.

Oh the man must have done it because women wouldn't lie about these things. Sure, good women don't, but women with bad characters and low morals do.
Every good person caught in the middle of this can pay a big price regardless of gender. They should focus more on separating credible and good principled people from the bad apples. It is more difficult to do that though when bad apples from the men side team up with bad apples from the women squad.
Of course, it's also much easier to use toxic ideology and paint everything with a broad stroke, than to actually treat each case separately and use universal logic and principles. You need intelligence for that, and intelligence comes in much shorter supply compared to a smartphone and a social media account.
So, if you believe one gender is naturally more principled than the other, you are a sexist idiot, regardless if you vote right or left.