It used to work quite well. Perhaps together you can think of a cause to the rift, and try to actively fight it instead of each other. Start with commonalities, not differences. I think it’s important to, at the very least, never stop trying.
The question assumes we know what someone believes before we've spoken to them. That's the actual problem here, people are being excluded based on assumed beliefs rather than demonstrated behaviour.
Opinions evolve through exposure to different viewpoints, not through isolation from them. The homophobes and racists of the 80s who changed their minds didn't do so because they were shut out of communities - they changed because they were forced to actually interact with the people they'd made assumptions about. That contact broke down the assumptions.
When you exclude someone pre-emptively because you've decided what they must believe, you've eliminated the possibility of that evolution happening. You've also replicated the exact mechanism that made 80s bigotry so pernicious: denying participation based on identity or assumed characteristics rather than actual conduct.
Everyone thinks they're right. The racists thought they were right. The homophobes thought they were right. You think you're right. I think I'm right. That's why behaviour-based boundaries matter more than belief-based ones. Judge people on what they actually do in the space, not what you assume they think.
If your moral framework requires everyone to already agree with you before they're allowed to participate, you're not building a community - you're enforcing an orthodoxy. And orthodoxies don't evolve, they just calcify.
How can society become less polarised if we normalise an extremely wide spectrum of different moral axioms? To reduce polarisation, people with extremist moral axioms must stop having them, which can't happen if extremist moral axioms are accepted.
For one, I think that the people you have put the "extreme" label on, are not as extreme as you think they are, and indeed could be quite agreeable when you'd seek them out and sit down with them over tea and try to communicate with them with more nuance than a 160 char message can deliver.
Yes, you will be able to find examples that confirm your statement, but they are an exceedingly small minority, probably despised (almost) as much by their "own group" (as far as people actually feel part of a group) as they are by you.
I believe it is the (incentives of) the (social)media and the bots that have made you believe otherwise, over time and in small steps.
I don't know if you notice what you're doing, but you're turning a low stakes / no confrontation situation into a high stakes / confrontational situation for no discernible benefit.
This type of self destructive behavior may seem worthwhile in the moment, but in the long run it doesn't bring any benefits, because you have to fight the people you're declaring war against and if the list of enemies is long enough, you're almost certainly guaranteed to lose against one of them.
