Personally, I think I'd have the self-discipline to stop myself from laughing in public, but I guess I might let myself laugh in private. I imagine that some people would not have the self-discipline to do that though.
I might say there are two kinds of jokes that feature offensive content: rhetorical and intentional. If it's rhetorical offense, it's "funny." It's clever or disarming enough to outshine its offensiveness to most listeners. Usually offensive jokes that aren't "funny" enough are intentional. They're meant to be offensive and start fights (many may unknowingly tell these jokes because other people told them they were all in good fun). There's also the matter of who the audience is. The post is aimed at the answerer, but settings change how someone responds. A group of like-minded pals: I'd laugh if the joke relatively suits my views, regardless of the kind of content. A mixed audience of associates: well...I'd be the same, basically, but I won't ignore if anyone is offended, only because I have a peeve for things that go ignored.
In any setting when jokes are so transparent you can tell they're 'off,' mean-spirited teases disguised as innocent jests, I'm not really interested. Not cuz these jokes are "wrong." They're overwhelmingly simplistic.
My opinion is that all funny jokes offend someone and therefore I would just laugh.
Which reminds me of when I watched a documentary about John Carpenter's Halloween. Someone in it said that the magic of horror movies was how much fun people had making them. The argument was that in comedies everyone is always very tense because not only the timing has to be perfect, the same thing that makes one laugh does not work for other person and might make another one offended, while in the horror genre everyone is laughing and excited about the next fictional death.
Off-color or dark jokes, appreciation; blatantly bigoted remark, distaste.
Conscientiously told to tailored audience, appreciation; carelessly told in public, distaste.
Family or friend, appreciation; distant acquaintance, distaste.
Typically I'll usually still vocalize something about the joke or them being messed up to say it but I still might get a good laugh out of it. I don't exempt myself - I crack jokes at the expense of myself and groups I belong to sometimes, too.
In general I don't find offensive humor funny. If it's really clever and it makes me laugh, I'll laugh. If it's boringly offensive or they're trying really hard to be offensive, it's just uncomfortable and stupid.
I was watching a roast type of thing, not the celebrities one, and one guy was constantly talking about the other guy's dead family members. I felt embarrassed for him. It wasn't funny at all, just stupid.