Almost no comedy will be inoffensive to everybody, and if it is it's probably pretty boring. With comedy you're relieving tension by saying and doing the unexpected, and a lot of times that by its nature will lead to people not liking the results or saying it's offensive to them — that your representation of their particular experience is unfair or inaccurate. That will always happen, but I think the likelihood of that happening is so greatly diminished when you're setting out as a performer or creator to try to be honest. Instead of just saying Okay, what's the first thought that comes to my head — what's the easiest stereotype I can make fun of? and then just going with that, thinking a little bit deeper and trying to understand the real motivations and attitudes and behaviors that make us human, and then looking at those things as the material you can focus the joke on — I think that's where the best comedy comes from and that's why people like Key and Peele are almost infallible. It'd be really tough to put together a legitimate case about them being lazy or insensitive comedians. They feel like humanists to me.
I like that notion: If you're coming across as human and digging deep and trying to understand people's genuine motivations and behaviors, it's gonna be tough for anyone to call you insensitive.