Is your main problem the topic of discussion (politics), or rather than the discussions have a tendency to go beyond casual consversation?
If you have an issue with the topic of politics,
then I'm afraid there's not much you can do.
In example 2, based on your description, the entire family actively wants to discuss politics. They're allowed to do so, especially if all of them wish to do so.
Similarly: If they were all into dancing instead of politics, it'd be okay for you to not dance; but it wouldn't be okay for you to tell them to stop dancing.
In example 1, your relative seems to bring up something about you (that just happens to contain a political opinion), rather than trying to discuss politics for the sake of discussing politics. The fact that he immediately opens up a conversation in a direct manner, seems to be done with comical intention (comically overplaying the importance of your opinion on drilling).
Similarly: I am someone with an outspoken opinion about disliking Apple and their products. I might open up a conversation with my friend (who bought his first iPhone) by saying something like "So, an iPhone, huh?". As long as it's clear I'm being comical, and the person actually gets the joke, I'm not being offensive nor am I trying to spark a heated debate.
You may not like discussing politics. But your interpersonal issue is essentially no different from disliking other topics of conversation. All my friends have recently bought and/or renovated a house. Since then, as the only friend in the circle who still rents a place, I feel fairly disinterested in the almost constant talk about mortgages and renovations. Being in this position, I have three choices:
- Avoid the friends, so that I can avoid the topic of discussion.
- Forcibly change the topic, or directly ask them to change topics.
- Accept that they are talking about something that is important to them, even if that means I'll be observing more than participating.
1 is not always viable, and even then it's still a bad solution. 2 is fairly rude; you don't get to decide what others want to talk about.
Which is why I chose option 3. I let them talk about it, and the topic of conversation has died down after a year (since most of them are doing other things now).
Unfortunately for you, politics is a neverending source of discussion. It's likely that the family will always find some political issue to discuss.
But if that it the case, then that also inherently proves that the family wishes to discuss politics, and you shouldn't be telling people what they are allowed to talk about.
I would suggest you don't get involved with the discussion, politely responding when someone addresses you directly but without trying to further the discussion.
Eventually, someone will recognize that you're not getting involved with the discussion, and will talk to you about something else (at least, that's been my experience in most close-knit social gatherings)
If you have an issue with the intensity of the discussion,
you have more of a say. Note that you still cannot ask people to not talk about politics. But you can address the nature of the discussion you're a part of.
- When first joining in the conversation, remark that you don't have a strong opinion on the topic. This makes it harder for someone to dig into a debate with you about how wrong you are (which is usually how political discussions derail).
- Only engage in a discussion when you want to. If you don't want to, remain polite but try to avoid furthering the discussion. People who engage in political discussions tend to look for opposing arguments. If you don't oppose their argument, they will generally not lock onto you as a discussion partner.
- If you don't want to engage in the discussion, consider the option of remaining an observer and not just walking away. It means that you're still participating in a social event, even if you're not adding much to the discussion. Maybe the discussion eventually reaches a more interesting focus for you, at which point you can chime in. Even if it doesn't, listening to others' argument will teach you about the person. You're still getting to know them, even if they don't quite get to know you because you're not an active part of the discussion.
- When someone tells you their (conflicting) opinion, focus on the positive parts of what they said (it's well-reasoned, you see that there is merit to that line of thinking, he's definitely not alone in thinking this way, ...) Do not point out flaws in their argument, that just puts fuel to the fire.
- When you feel that the discussion is getting out of hand, you can mention that. Mention that you're out of your comfort zone, or that you're not really able to discuss the nitty gritty details, or that you feel it's not the right time to go over the finer points.