It's hard to say. I think the closest I've deny come to that decision was when Dave Grohl denied AIDS. He's a fucking idiot for that, but it hasn't stopped me enjoying Foo Fighters. None of the artists I listen to have expressed any antivax views yet, as far as I'm aware, so I'd have to cross that bridge when I come to it. I don't think it would stop me enjoying their music as I believe in separating the art from the artist, unless they've done something unspeakably evil (like that bloke out the Lostprophets for example, not that I was ever a fan of theirs personally).
Going to their gigs might be a different matter if it means there's more likely to be anti-vaxxers who could spread the virus, but a) just because that's what the artist believes doesn't necessarily mean the fans agree and b) I don't know that the bands have any control over who can and can't come in, as it's all bouncers these days anyway!