Have you seen the series Frank's Place (1987-1988)?

Except for a few episodes on YouTube, I haven't seen the show since its original broadcast. The creator Hugh Wilson (WKRP in Cincinnati) was White; Tim Meadows (the lead, also from WKRP) wrote one of the stories (most but not all the writers, from what I can tell, were White).

I'm going from memory here, but even though much of the humor was based on racial (sometimes intraracial) conflict, it was always respectful of its characters, and never took the short-cut to a punchline.

In my opinion, it's possible to make a timeless sitcom episode that contains race-based humor--just very, very difficult. And (based on my memory of Frank's Place) it's no excuse if the time was long ago, or the writer or director was White.