This is interesting to talk about because it's a pretty unique situation. Other decentralized systems have converged on a single globally connected network everyone uses; either everyone can visit your website or your website is irrelevant. (You're either allowed on Twitter or banned from Twitter.) Individual blocks exist but they aren't widespread enough to break the whole network into pieces.
The closest comparison I can think of is when Russia disconnected itself from the Internet. Everyone was still nominally part of "the Internet", they all still used globally unique domain names and IP addresses and stuff, but suddenly Russians could only access Russian websites and non-Russians could only access non-Russian websites.
This is essential to how people conceptualize disagreement. At the root of the disagreement is something sacred, something taboo, which cannot be openly discussed. Some people consider others to be closer or further from the taboo. Other people think that there is a line that divides incompatible views about the taboo.
The immediate reaction to this description is very likely to be a misunderstanding if you think about it in the context of an actual divide. Nobody is above the taboo, including you, although everybody thinks they are above the taboo. You cannot escape it with "logical thinking", because both sides conceptualize the taboo in incompatible ways. The logical thinking happens within this conceptualization. The immediate reaction is to blame one of the sides of the discussion of misunderstanding.
At the same time, I'm not sure what framing other people approach social interaction but not once do I think things like "left", "right", or "sides"... "divide". I'm nearing 40 years old and still don't understand rationally why people lean towards these simplistic labels when people in general don't nicely fit them at all. I'll see some toot I don't like and think "oh, don't wanna see that sh*", block the user or perhaps the whole instance (if it's one where most people posting there share such stuff I don't like to see). The specific political stance of the person or instance won't even cross my mind, because why do I care? I just didn't want to see some racist or hate-propagating BS, regardless of where it's coming from or what ideologies it could be associated with.
Anyway, just my $0.02 on this topic; I didn't want to see this kind of polarizing perspective go unchallenged.