This post is inspired by the Atlantic Article called "If You Must Talk Politics at Thanksgiving, Here's How: 10 Unsatisfying Rules For Disagreeing With Friends and Families Over the Holidays."
Their suggestions are good advice for any time of year, although I'd recommend avoiding any and all serious discussion during a holiday if you possibly can. It's a time to be welcoming our nearest and dearest, not driving them away.
Still... I am aware that some of us have friends, neighbors, community members, or relations who just cannot be discouraged from venting at our political affiliation, religion, or other differences. Then you have but few (angelic) choices: refuse to discuss it, defend yourself respectfully, leave or ask them to leave (if it is your house.)
If you find yourself tempted into the fray, then may these tips be of some help to you. This is how I try to approach such discussions (though I'll admit I don't always handle it perfectly either.)
The basic strategy here boils down to respecting the person even when you don't agree with them at all. This may mean ignoring what can seem like a personal attack on your status in the group and your personal worth. Even if a personal attack is exactly what is intended, it never helps to point this aspect out. It's not about who is right or wrong, but surviving until dessert is served. You need a fire extinguisher, not gasoline.
My tips: It is helpful if you make an effort to acknowledge all valid points from the other side, and accept in advance that the most you are ever going to do is sow some seeds of doubt in the 100% rightness of their position. Never even hope you can change the other person's mind entirely, as that way endless debates and acrimony loom. The other side assumes that nothing will do but their total submission to your incredible wisdom, and that just ain't gonna happen, Hoss.
Stick with demanding a little respect for your differences - and let the rest go. Say what you think is the most important parts of why you believe/live as you do, back it up with what facts you have, and (ideally) look for the earliest moment to end the debate in a way that is respectful to both sides...without retreat...without hard feelings. Grit your teeth if you must, but realize this is the best gift of peace and love you can offer to everyone at the gathering. It is the wise thing to do.
Family fights are memorable but NOT great for cozy holiday memories, which is why debates like this should be avoided whenever possible, and ended quickly when they arise, as long as this doesn't steamroll others' self-worth.
Opinions are like noses, everybody has one and they all drop *ahem* less than delightful offerings from time to time. Yeah...eeeeewwww
(and a tissue box)