BLM isn't really a monolithic entity, of course. No movement really is. They'll go for different candidates. Worth pointing out that when BLM disrupted the Sanders rally, Sanders was deferential to their cause - i.e., disappointed he didn't speak, but supportive of them all the same.

The larger point is that the far-left's anti-speech crusades are starting to alarm a large number of people on the left. As well they should. When organizations have as their goal to silence people - vast swaths of people, in these cases - that is a chilling thing. If politicians support their shutdown methods, those groups will then expect those politicians to do the same, legislatively, once in office. And if they don't get their way, what will they do? If they're willing to try and ensure somebody never gets to speak, 1) what is the difference between society shutting down your speech and the government doing it, and 2) what ends will they stop at to achieve this? Dershowitz, I'm quite sure, understands whose obligations are what under the 1A, but it's also true that society has the power to shut down speech it doesn't like, which itself is rather chilling.