> The word you're looking for is stereotype.

Sure, but that doesn't change anything. That some people will be unfairly characterized by this is an unfortunate byproduct of being born a human.

> There's lots of harmful and inaccurate stereotypes about all groups of people out there, and polite society generally frowns on using them as a form of bigotry.

Only the bigoted forms :) stereotypes aren't going to disappear out of inconvenience

> In fact, actual in class socialization is frowned on or punished in most schools.

I've never heard of a school that could combat socialization in any meaningful way.