One way to avoid this, of course, would be to agree among yourselves that you simply weren't going to talk about politics. You may even be able to suggest this in advance to one or two people who can influence others.
However, I know this may not be realistic; you may even have one or two people in your family who actually enjoy causing controversy! Plan games and other activities to keep people busy, and if necessary try to steer the conversation in other directions. If someone brings up politics, you might even say with a smile on your face, "Now you know we always get into an argument over this. Let's instead make this a happy time!" The Bible says, "It is to a man's honor to avoid strife, but every fool is quick to quarrel" (Proverbs 20:3).
Why not use this as an occasion to help your family think about the meaning of this special holiday? Before you eat, pause as a family to pray - and as you lead them, thank God for the freedoms we enjoy, and for the sacrifices of those who gave their lives to purchase it. Thank God, too, for your family, and ask for His blessing on them.
Not only will this turn your family's hearts to the true meaning of this holiday, but it could also set the tone for your whole gathering and make it a time of peace and thanksgiving.