It's a tricky one.
I'm trying out a new mindset this year: be kind. It's not up to me to think I know better than someone else - what I see is a tiny facet of their whole personality, and they have many layers supporting and amending the belief that I have an issue with.
I can choose not to donate money to a cause I do not believe in, but to refuse pay a reasonable amount of money for something just because a small amount might be spent on something I disapprove of is over-complicating my life.
As for the OP, like Pico I try to separate actors from roles. In fact I often get a crush on an actor for a specific role but have no interest in watching/ reading their interviews or promotional pieces. Actually, I've just been scanning my mind for examples and found that when I am really fascinated by a role, I usually do watch the actor in other situations. Damn. That's because all the ones that immediately come to mind have made a big impression on me. Blackadder, Dr Peter Venkman, Cher Horowitz, Han Solo (see below), Captain Jacks (Sparrow, Harkness, Morgan) Tim Bisley, the 10th Doctor etc etc.
I remember with deep, deep shame when
Six Days, Seven Nights came out. I refused to see it because Anne Heche was playing a straight woman. I decided she was "Selling Out" (because of course there are so many LGBT roles out there) and anyway I wouldn't be able to believe it. What an arse. Apart from anything else I didn't even take into consideration that Heche is bisexual. But worse, I looked at sexuality first and profession second.
I don't think I really missed out on anything by not seeing the film though