"Movements" inevitably draw dipshits. The Occupy Movement, the Tea Party, MAGA and Qanon, Pro-Palestine, Pro-Israel, No Nukes, Save the Whales, Critical Mass....you name it, I've seen em all over the past 50 years, and every single one of them ends up attracting some Grade-A dipshits. I remember many years ago, the Critical Mass group (remember them? They were kinda sorta a radical group for the rights of bicyclists to be on the road?) was doing one of its periodic group rides through the streets as a protest to slow traffic. A newspaper reporter rode along with them, and they ended up chanting or calling for a variety of things....including, when they rode by the animal shelter, some of them calling to "liberate the animals!" Made it clear that the group - while it had some defined ideals with some sort of merit - was also a magnet for generally disaffected people who just wanted to start shit.
This movement is not materially better or worse than any of the others. There's plenty in it, and in its basis, that has merit (I mean....Israel IS killing the fuck out of Palestinian civilians, and I think it's a decent moral decision to speak out against that and to try to put pressure on things and people who might help change that), but it draws the dipshits: the extremists, the lost folks looking for a place to call home, the gullible, the dudes going along with stupid shit because they think it'll get them laid (I remember well a story that Michael Caine told about going to a bonafide communist rally, just because he was trying to shag a girl who was going). All of this shit shakes out in the end. A lot of the radicalized dipshits will move on to something else -- or to nothing else at all -- in short order. They always do.
What the gov't shouldn't do is give them more credit or attention than they are due. Not less, either. Want to get the Columbia students out of the building? Go on in, arrest them, and drag them out. If they resist with violence, have your body cams on, capture it, restrain them, arrest them, and add that to the charges. But as to the ones who aren't really starting any shit? Leave 'em be. Lack of attention will destroy them. AND, in the process, also respect the Constitution, which is kinda important.