Great question! This one hits a little close to home.
I grew up listening to Bill Cosby, first on dad's vinyl collection, then on VHS, then on The Cosby Show, and ultimately live & in person. I'm no prude, but I think it takes an additional element of skill to make a body of people laugh while keeping swearing and crassness to a minimum, and Cosby could do that. I showed up for the comedy; I stayed for the craftsmanship.
Then all the evidence about his misgivings w/the womenfolk started coming to light, and the pedestal that I had put Cosby upon came crashing down. There's little in this world that takes me from zero to white-hot rage than sexual assault. I've seen far too many of my friends deal with it in their lives and the hellish reality that the scars frequently lead to. Nothing's been proven in a court of law, but there's far too much evidence out there against the man now for me to believe that *nothing* happened, so I'm left with reconciling the image I had of Cosby with the reality that he's likely a rapist.
I can't support that, I can't support him, and while I haven't yet, I'll be deleting all his tracks from my iPod simply because hearing his bits creates more cognitive dissonance in my head than I want to deal with when listening to comedy.
To muddy the waters slightly, let's turn to the Sandusky/Paterno/Penn State thing. I was born in Ohio which means I was raised on football and Ohio State. Frankly that team is the one I'd be focusing since they've had their fair share of thugs and idiots come through the program and Tressell cheated his way out of big college football effectively for life, but on the relative scale of shit the Penn State scandal makes Ohio State's trail of past miscreants look benign. Fact is, as long as they're not playing OSU, I love me some Penn State & Joe Paterno. I enjoyed watching their teams of the late 80's and early to mid-90's, and I think Joe's probably positively impacted more young men in his lifetime than the vast majority of our world's population.
And then Sandusky's crimes came to light, and with it the legend of Paterno started to unravel a bit. There's no doubt in my mind that Paterno new/saw something that Sandusky was doing at some point and that he knew Sandusky's actions were both illegal and dispicable. I'm also quite sure that Paterno didn't do enough to make sure those actions came to light at that time or to protect those boys. Do I think less of Paterno for it? Yes. Do I think of him as I do Cosby? No. Would I have supported Penn State if Paterno were allowed to continue coaching? Hmmm...that's the real question for me. I chewed on this long and hard while the investigation/trial was going on, and where I ultimately ended up is that I don't think I would have stoppped rooting for Penn State or Paterno had he been younger & remained there. My suspicion is that he regreted not doing more, that his lack of action is not in keeping with his true character, and that a couple of (admittedly terrible) mistakes don't constitute a pattern of awful nor are they enough to make me toss asside his decades of what I perceive to be good work with young people.
For a moment, though, let's say that I think Paterno is indeed an awful person and that Penn State should give him the boot, but doesn't. Do I still root for the laundry even though the leaders are dreadful? Probably not. At that point I'd probably label the school as condoning child abuse until both Paterno and the leaders were removed from power and the school did what they could to make things right.
To speak to some of the examples thrown out by others....Polanski? Nope, can't do it. I've seen none of his films, nor will I. Allen? I don't feel quite as strongly, but I still feel a little creepy when I see one of his films.
As for artists who take a stand on a social/political issue...for the most part I really don't care. I may think they're silly for supporting/not supporting something, but rarely if ever do I go so far as to expunge their work from my life for such reasons. As evidence, I offer the litany of artists who boycotted Arizona - my current home state - when we passed SB1070. As a 30+ year Arizonan I hate illegal immigration, but that bill was a special blend of idiocy and had no business being passed. But do I care that artists and other such folks boycotted my state? Not really. I thought it was silly for most of them to do so because most of them didn't fully understand nor appreciate the problems it was attempting to address or why the state congress passed it in the first place. By and large it was a bunch of kneejerk reactions that ammounted to "You're a bunch of racists so we're not going to your state," and if they believed that to be true then I applaud them for exercising their rights. I didn't boycott them, though, and didn't think too much of it beyond that. Silly, largely ineffectual, and largely needless, but whatever. Go make art.
And honestly, a lot of art does have political/social underpinings or inspirations. Take Springstein for example. If you were a fan of The Boss in NC before he cancelled his show, why would you stop being a fan afterwards? He's never been one to shy away from social issues. Same with Clooney. If you were a fan of his work and a conservative before he started doing six-figure dinners for Democrats, were you not aware of his liberal/social work prior to that? Why would a politically-motivated dinner make you more upset than his other politically/socially-motivated work?
In short, I think it's probably a little silly to boycott artists or athletes based on their politics or social stances since we all have beliefs and don't want/need to be skewered for those. I do draw a line, however, at murder and crimes against women and children.