As you say there is a toxic culture in some places and if you stand up and fight besides these people you have lost, or if they fight for you cause. It's a common problem.
Nope, it doesn't work that way. You're just wrong, sorry, you lose.
See what happened there? You used a tactic that works mostly against people who avoid confrontation. Why is gamergate still a thing after all these weeks? Because SJW tactics don't work against people who seek confrontation online, and are used to achieving their goals by endlessly grinding, week after week, until they win.
You will not succeed in convincing all "gamers" that an ugly stereotype applies to them. Best give up now.