Depends, really.
As an example, the CEO of a company that makes products I like has been shown to have donated quite a large sum of money to an anti-gay cause. I won’t be buying that company’s products any more.
If I found out something similar in the arts, I’d do the same thing. But there’s a difference between a person believing incredibly stupid but basically harmless stuff like “the moon landings were faked” and someone actively supporting an evil cause.
I don’t know and don’t care. It doesn’t even bother me that Tom Cruise and John Travolta are Scientologists. It doesn’t come across in their films (well, forget Battlefield Earth) and is largely irrelevant to me.
Disclaimer: I am not a Scientologist and do not subscribe to their beliefs. I just prefer to look the other way and not hold it against someone I like.
I don’t really want to know because as a poster above said it would have an effect. Kipling, who may be my favorite author, was definately a prejudiced bigot based on some of his US travel writing. I’ve argued here on the boards and elsewhere that his Indian works was not racist. Still learning that part of him was an ugly truth I didn’t really want to know.
On the flip side, I think Freda Kahlohas a lot more attention on her work and admirers than her art justifies because her husband was a quite the jerk with her.
I don’t care about the artists but I do care about the MILF belly dancers. What kind of church revolves around that? Maybe I can still find religion.
I like it when I find out they are a (non-fundie) Christian. I don’t mind finding out if they are atheist/agnostic. Anything else religious kinda bugs me.
Politically: only if they are fairly moderate. Really, all that bugs me is extremists. And Scientology.
Wait, forgot my biggest hate: those into woo. That’s worse than finding out they are a fundie tea partier, for some reason.
I don’t care what they are, and knowing what they are doesn’t bother me.
But if they won’t shut up about it, especially if it’s opinions I disagree with, I am disappointed.
I don’t generally *mind *knowing. But I don’t go looking to find out, if you know what I mean.
The church doesn’t REVOLVE around the belly dancers. They rent a room from us and are around two or three times a week. Nor are all of them milfs, but enough are to make me frequently happy. 
Nope, smaller band, nobody very well known.
Leaving actors & singers out of it for the moment, how do you feel an author or painter’s views distort their work?
Well, the ending of The Jungle would probably have been better if Upton Sinclair had not turned it into a political screed.
Exactly what I came in to say.
I like to know. In the case of writers, artists, and musicians, knowing their political, social, or religious beliefs often adds to my understanding or appreciation of their work. I notice things that I wouldn’t otherwise.
Now, in some cases that means avoiding the work of someone I might otherwise be interested in. I’ve never read anything by Orson Scott Card, for instance, and once I found out that he’s a crazy, moronic jerk I lost interest in anything he had to say.
It really pees me off when someone who is attractive to look at and whos main ability in life is to entertain people, considers this to give them a blank cheque to lecture me and others on moral, political and ethical issues.
The ones who really make me go all stabby are cocaine using comedians (Sorry commentators on life, or whatever crap they like to call themselves at the moment) who preach to me about the third world, starvation deprivation and all the other subjects that they are so personally knowledgeable about)
I try not to financially support evil, so I’d prefer to know if my favourite artist of the moment is a cherished donor of Puppy-Killing Fascists Inc so I can avoid giving them money in the future.
Other than that, I don’t really want to know anything about them. The risk of it sullying my enjoyment of their work is too high.
I generally avoid watching or listening to actors being interviewed. I don’t care about anything they may or may not believe, and I don’t want their real lives intruding on my movie watching experience.
When I buy art at shows, I tend to avoid talking to the artists. I couple of times I’ve discovered the artist is a jerk, and then failed to buy the piece I was looking forward to buying. I’m sure I’ve missed on meeting some nice artists because of this policy, and I’m sorry for that.