On one hand, I always want to keep an open mind about religion and politics, and I'm always interested in hearing what others are passionate about, even if it's in those topics. That's how I've learned so much of what I have.
If everyone followed the rule of avoiding these topics, I wonder how many people would never hear an opposing opinion, maybe even a more beneficial one, to the one they've grown up with. I think these topics should be encouraged.
That said, the moment you disagree with someone on one of these topics, some people will definitely fly into a small rage, or instantly cut off contact with you, or even slander you to others, or some mix of these.
Ultimately, I think that's fine. For one thing, you have just learned that this is someone you probably don't want in your life anyway, because they can't handle disagreement in a civil way.
And you learned it fairly quickly and at a small cost. Even if they slander you, people whose opinions you'd actually care about will generously take their word with a large dose of salt, especially based on their character, since such a character usually has other tells too.
So my current stance is to just be open to these topics.
Just yesterday, while I was sitting here at the library, someone approached me and asked me to watch his phone while he used the restroom, in case ICE came in and took it. He was joking, but we went into a slight conversation about politics in general, in which we found out that we disagree on certain topics, and he almost took offense at me disagreeing. I was friendly and open to him the whole time, and he was friendly when he left to use the restroom. But when he came back and sat back down, and later left the whole library, he left without even so much as a goodbye or wave. It seems like he just didn't like me anymore because of my disagreement. And that's fine with me. Both would have been fine.