Maybe ask some Asian people if people have ever assumed they know martial arts, and if they’ve ever been bullied or harassed because of it. It’s quite common. Perhaps especially so in America? Regardless, the stereotype exists and causes harm whether you live in a place where it’s frequently happening or not.
They’re not specifically coded as anything. They are very loosely based on Western folklore, but they are not presented as explicitly European. You could maybe argue that the Druid is vaguely Celtic, but the actual Celtic mythological influences in the class are minimal. Monk is the only Class with a sidebar about reskinning weapons to fit a certain cultural aesthetic. It’s the only class that has a feature named for a concept from a specific religion. It is clearly coded in a way that other classes are not. That coding is racial and not cultural because the Monk’s influences are a vague pan-Asian mishmash, not any particular culture (though Indian influences are conspicuously absent). It’s textbook orientalism.
I think that would be a problem, if barbarians were more modeled after any particular real-world groups. Like, if they were black coded, or Native American coded, or otherwise coded in a similar way to how Monks are Oriental coded, yeah, that would be more egregious.