A big problem is the anti-regers lead/heavily influence most of the teams 🙂 The titans'll listen to Dick, JLA Batman, Outsiders Alfred, etc.. The Wonder clan will go with whatever side they think is more right, and furthermore are associated with a government that was at least once part of the UN that'll object to it. Superman I can see basically refereeing and making sure neither side goes too far.
Also the JSA were presented with this very choice way back, and they all quit rather than sign up. So Alan Scott, Jay Garrick, etc.? They're anti-reg, and most of the rest of the JSA is likely to follow them.
I think what they'll try and do is collectively ride out the public backlash, fighting crime, while appealing to the public openly and more actively than the Marvel anti-reggers would. They'd pull out stuff like various government black op super programs, of which they have a lot of experience with, have Mr. Terrific vouch that Checkmate can do it's job without the registration and has done so fine, etc. etc..
I don't think it turning into open violence as much, and the hero community won't be as split. More neutrals, more communication.