I don't like my uncle staying at our house
Why don't you like him staying there?
I'm uncomfortable with his conservative values
That sounds difficult for sure! It's always a bit hard when you're around people that don't share your views and values, but he's your Uncle and most people would expect you to at least let him stay until he's back on his feet.
But I feel like I owe him everything...
If you have a conversation with him about what's wrong and right to say around you, then it could save a lot of awkward conversations. Just make political talk something you disapprove of and this should solve itself!