I see a leap in logic in your OP example, and I don’t know if it’s yours or hers. Does your wife actually enjoy the actual concept of killing? Having shot something yourself doesn’t mean you do. She could have shot it because she liked venison and as part of a conservation effort. She could do it because she enjoys the skill involved. I’ve actually only met two hunters in my life that enjoyed the process of killing itself–and they also were the type to torture animals as kids.
But if you really do enjoy the process of ending the life of other creatures, I think that is a legitimate reason to not be friends. I likewise will not be friends with anyone who is bigoted towards the mentally ill. I’d say bigots in general, but I’m temporarily allowing for reluctant bigotry based on religion–though I will fight it. And I allow for harmless leftover bigotry in really old people.
I will also not be friends with someone who I catch bullying other people–though you might argue that’s not a belief issue. Other than that, I’m more “don’t ask, don’t tell.”
Unless you count people who think The Great Gatsby is actually a decent story. Then you’re dead (off screen) to me.