As in just about every case, recognising the problem is the first step. I personally see that I have contributed, in part, to various let's call them as you say dramas, and have concluded that some times the best option is the "ignore" button. Now I'm not saying that's always the thing to do and it's not the only option, but I've tried staying out of fights, ignoring (not with the button, just not responding to) people I don't get on with or who don't get on with me, but eventually after some effort have found the only way to address the problem was to hit the "Ignore".
Of course, you can't have everyone doing that otherwise nobody will be able to talk to anyone!
So how to proceed? Hmm, I don't know. Well, let's see, just throwing this out here, see who thinks what of it: how about, I don't know, acting like adults instead of children?
I'm serious. Much of the cliquey behaviour you're describing -- correctly --- here duga is down to the old playground "my mates against your mates" mentality, so that if one person gets slighted all their "gang" retaliate and suddenly there's almost a forum war going on. Then the original "offender" has his or her gang weigh in on their side, and off we go again.
People should be able to work out their differences peacefully and without recourse to stupid namecalling, one-liners, smileys, GIFs and memes. Sometimes all it takes is for one person to explain to the other that they took them up wrong, and as Elton said, sometimes sorry does seem to be the hardest word. Nobody will admit they were wrong, nobody will apologise. People go on and on exhibiting the same unacceptable behaviour, encouraging others to do the same, and the whole vicious circle turns.
This will sound a really stupid idea, but in the absence of any other ideas, what would anyone think of a sort of "grievances committee", maybe a thread where two people with a problem could put their case and members, either random or more likely some sort of, for want of another word, jury, could rule on it, then whatever was decided the two members would have to abide by, on pain of a ban, and maybe permaban if they kept ignoring the decision.
Something very simple: one member keeps calling the other gay. He/she doesn't mean it but the other one gets annoyed. Rather than this escalate the "committee" rules member 1 should not call member 2 gay. If member 1 does, he or she is banned. Yeah, I know, idiotic, but I can't think of anything else.
Really, people shoudl not need to be policed though. Simple human common courtesy should be a byword of this forum, and really everyone should treat people here as they would were they to meet them in real life.
Not that they will, but it's a good maxim, if only people would follow it.
Of course, another solution for an infraction of the decision of the committee could be a "group ignore". Have you ever heard of sending someone to Coventry? Basically everyone ignores them for a set time --- not long, say a day, maybe and perhaps they might get the idea?
Yeah, all bad ideas but who's coming up with anything better?