I can often find the humour in something and find it funny at least to a degree. I've yet to come across something that's intended to be funny that I find offensive (but I'm a 20 year old straight white Christian guy so I doubt that will ever really happen). The picture you posted, has a humourous tinge to it, I mean it's a controversial topic put to the Pokemon theme, ha ha, but after reading it once I don't find it funny anymore, partially because it's an old trick and partially because it's controversial. I suppose I do have a dark sense of humour, I find a lot of sexist jokes hilarious, so long as they're done right, but if something has very little humourous merit other than being controversial, I don't really find it funny, such as the picture you posted.
As to other people's humour, if something is clearly controversial I won't try to impress on anyone how it's funny because I understand my sense of humour is different to others', even if the controversy doesn't necessarily apply to them. I dislike people going off on a rage over something like the picture posted because it is a joke, it's obviously completely taste-less but that should be more reason to just ignore it because chances are it was done to get a rise out of people. But, like I said, I'm not really part of any minority so I'm not going to tell someone else how to take a joke that they find offensive. HOWEVER, people who aren't part of the minority who rage against it FOR them annoy me most.