If my coworkers were harboring opinions being against certain races (i.e. racism) that they simply didn't say out loud, I would certainly feel deeply uncomfortable being in their presence, and that absolutely affects my work week. Telling people to just not talk about it doesn't really make that any better: in fact, it probably makes it worse.
> In the scenario you describe, how would you be aware of their racism if they didn't discuss it at work?
Well, I suppose if there were no minority employees in that workplace, it would be kind of hard to tell, but otherwise, it often isn't that hard. And if you are in the minority, you almost certainly can tell since, in a thousand tiny subtle ways, you're constantly being told you don't belong.
If they didn't say it out loud how would you even know, and what does it mean to harbor feelings? You read their diary? Saw it in their eyes? Used your intuition?
Aren't you worried you could be wrong if that's the standard, or someone could use that standard against you and be wrong?