I have two relatives who are about as far apart from each other on the political spectrum as you can get. We've outlawed political talk at family gatherings, but these two always seem to manage to pick at least one political fight with each other. And then complain that the other one is unreasonable. 
Last year, I changed the subject several times when they got into it and they both managed to bring things back to politics. Other family members actually commented that they were astounded by how dogged these two were in refusing to let me change the subject.
This year, I will change the topic once. If they don't let it drop, I'm going to get up and walk out of the room. I love my family, but I think that I'll love them even more if I don't have to listen to them fight with each other.
My grandfather is like this though the only person who really riles him up is my dad's best friend, basically my dad's surrogate brother. One summer they left both of them alone with me, brother, and cousin (I think we were around ten at the time). I don't remember the argument but I do remember it was about 5 hours and went past sunset.
Anyway to stop the political shenanigans you don't change the subject you stop the subject. Use words like "you are ruining the holiday." At least thats what my mom does to get my grandpa to stop.
Mind you it doesn't help when other relatives purposely antagonize him.
We have an Angry Uncle in my family who has extreme views about well... everything. Religion, politics, sexuality, TV, gun control, international adoption, the recipe for Twinkie filling- any conversational topic can turn in to an all-out screaming rant. The funny thing is, no one IS actually arguing with him. We all learned a long time ago not to engage. But still, every holiday is marked by ranting and raving loud enough to wake sleeping babies three roooms away, before the pie can even be served.
Last Thanksgiving I'd had enough. Uncle was yelling about education funding and I got up and left the dining room table in the middle of the meal to eat in the living room to eat with the kids. He wasn't ranting at me, just his "general audience." It was one of those weird, out of body moments where you haven't necessarily made a decision, but your limbs are moving you in a certain direction. I was just so tired of it and upset and frustrated, the next thing I knew, I was walking with a plate in my hands.
Was I rude? Possibly. To be honest, Uncle barely noticed I left and as soon as I was settled at the kids table, started his education funding rant anew. A few minutes later husband joined me in the living room, as did two aunts. If the meal had gone on longer, I think Uncle would have been the only person left at the table.
This year, we won't have to worry about it, as Angry Uncle has divorced out of the family. (A megathread unto itself.)