I did ask myself the same question tbf, however I thought of
Harry and Paul with the Nelson Mandela sketch. I'll link it below if you haven't seen it. If it's just a cast of two, how do you deal with playing other races? Other than just not doing it, it's hard to imagine how it could be done. You can't just bring in a black person to play them for one sketch, it's supposed to be just those two after all.
With Little Britain I get that they're trying to parody mid-2000s Britain, but I think some of the humour was misplaced.
The black character in the fat suit, for example. You could make them white and nothing would change, so you can't say the blackface was required artistically like with the Mandela costume. Like I said above, context is important, and I'd be much more willing to look the other way at the Harry Enfield sketch. It dervies comedy from the fact that a well-renowned peaceful and virtuous person like Nelson Mandela is played as a drug pusher. It's that juxtaposition that makes it funny, as the audience is aware of the contrast with his real life persona. The blackface is secondary, just to pull off the look of the character. Acceptable in 2020? Not for me to say, but probably not. With Little Britain, it was poking fun at the fact that '
ha ha, we've put this person in a black suit', which to me seems more offensive.
As for how you tackle that as two white men making a sketch show? I guess you don't, unless you've got a really good reason and are prepared to argue it.
Link: