For just one thing, the First Amendment and the rest of the Bill of Rights applies only to government. Message board owners are perfectly free to ban hate speech and many do. Private citizens are perfectly free to tell people to STFU or go elsewhere. Hell, even governments, to which the Bill of Rights DOES apply, punish hate speech.
The real issue is why so many board owners seem reluctant to include speech that hurts women with speech that hurts members of other groups that have been discriminated against historically in this country. What would not be allowed as to people of color, Hispanics, religious minorities, members of the GLBT community, etc. is allowed as to women. Why?
Is it because no one moves out of a neighborhood because a woman moves in? Is it because board owners are male? (I've been on boards run by women who censored racism, but not genderism.)
I don't know the reason. But it is not that civil liberties or free speech would end. Or even that there's nothing else to discuss on a political message board if posters can't post hateful, condescending, etc. things about women.