There was actually a fair amount of stuff about race in there- Carlton being mocked for acting "too white", Will & Carlton being arrested after driving too slow in a sports car, etc.

But they also balanced it out. Like how after Aunt Viv got black history being taught in the private school, Will & Carlton treated it like a goof-off class while the white kids were super into it- even doing extra credit stuff.

There weren't a lot of while people in that show (zero of the main cast) but most weren't portrayed as racist.