Whenever I discover that someone has a radically different viewpoint or opinion than my own on some particular topic, a few things always happen in my head, in roughly this order:
First, I double-check the disagreement to make sure it’s real. Sometimes there are miscommunications, differing definitions of terms, etc. If someone else’s position is radically different from my own, I like to be certain about it.
The next thing that happens is that I give some serious consideration to whether my own viewpoint should change. Philosophical positions have a sort of gravity to them, and when I encounter one of particularly deep conviction I think it’s hubris to not at least consider the possibility that I’m the incorrect one. I like to think I have good reasons to hold the positions that I do, but part of what gives me that confidence is avoiding echo chambers and listening to dissent.
Assuming I choose to remain in my own position, however, the next thing that happens is that I briefly entertain the notion of trying to sway the other person out of theirs. The instinct to do so is strong, but I generally fight down that instinct and resist the temptation to argue.
So then comes the last step, the most enjoyable one – I look for ways to profit from the disagreement.
Not just for me! I’m always looking for win/win scenarios. Opportunities to help each other and both gain more than we spent in terms of juice. The thing is, that’s actually less likely to happen with someone who is in agreement with you on most things. When you find someone who has a very different mindset than you, there are all sorts of things you can do for each other to take advantage of each other’s strengths and their ability to counteract your own weaknesses.
So don’t dismiss people who disagree with you. Don’t bother trying to change their minds too much, either. Just look for the ways you can each profit from the friction. Life is more interesting that way.