Well, it depends on why I dislike them. If they're just a bit annoying, or I'm convinced they could never understand me, the revelation of a common interest will thaw what frosty attitude I might otherwise harbor.
If it's someone who is an unrepentant criminal, I'm not going to let that temper the joy I find in my interests. But if, say, someone defends sexual harassment in the comic book industry, then when I call him out on that, he responds by sexually harassing me... and shows zero remorse (yes, that really happened to me), I know that our common interest in creating comics won't salvage that relationship.