All the evidence indicates that people get harassed when they publicly advocate and advance a political agenda that is strongly opposed by another group, regardless of whether they are male or female, black or white.
Sam Harris, a white "privileged" male, has received death threats and other forms of harassment from Christians for his stance on Christianity, from Muslims for his stance on Islam, from the left for his stance on Islam, etc.
Right wing Christian political candidates who oppose gay rights and support a right-wing Christian agenda are harassed, sometimes in a very vulgar and sexual nature, and sometimes given death threats (see Rick Sanatorium for a prime example).
Richard Carrier gives a talk about atheism plus and is harassed (take a look at the youtube comments here. Some of them are sexual in nature. For example: "This man has no penis. Which is strange for a man named Dick Carrier."
https://www.youtube.com/watch?v=au2i3xxgv7U
Where is the evidence (not just anecdotal stuff), that a male advocating the exact same things is harassed far less or the harassment is much milder in comparison?
This is not to say that the harassment isn't a problem that needs to be dealt with (before someone tries to spin the topic like this). Rather that the harassment is somehow exclusively a male problem against females who speak up on feminist issues that the misogynistic males disagree with.