It's also one of the many things about living in a world completely riddled with built-in privilege and prejudice that skews the pitch for everyone (almost everyone). And we do. Women and other minorities have been and are, routinely shouted down purely because they say something the shouter disagrees with, they're identified as belonging to the minority and summarily bawled at and degraded on that basis or cold-shouldered, until they fuck off.
It works both ways and good-hearted people, in all groups, are hoodwinked into joining pile-ons simply because of conditioning. All worth keeping in mind, that. This is not confined to twitter.