Honestly, it would be interesting if someone actually had a well thought out, non-racist reasoning for why they support free speech for those advocating racial genocide but not for those advocating for fair treatment by the state.
If such a thing were possible
Here's my try (not an American btw):
I value freedom of expression above almost all else. Almost because i value non initiation of violence more. If one individual or group is being violent, you do have to fight back.
I value freedom of expression because from my understand people, including myself, must be free to speak their mind, so it can change others and be changed. I agree that some speech is harmful, but i find banning good speech far more harmful. And while there's some speech that most would agree is harmful, i prefer to not set a precedent where a speech people disagree can be banned, as it can lead to good speech being banned.
So, my point is: i must defend the right to bad speech so i can have the right to my good speech.
That's why i argue in favor of the Nazi's right to speech. But that does not mean i don't disagree with their speech, i do, a lot.
Now i hold BLM to the exact same standard of free speech. I do believe they have the right to it, and defend that, and i also believe they have the right to shut down a freeway (not sure what your law says about it, but i still think it is a worthwhile right).
But... Just because i agree that they have the right to it, and i do agree with what i think it is the message they want to convey, that i agree with the way they are doing it. I think blocking a freeway is not the best approach to be heard, but in no way is worth a death by car.
So it is possible that i could criticize BLM more then the Nazi, not because of the content of the message, but because the way it is being passed. Nazi's ideas are despicable, and most people around me already agree with that, there's just not much point in discussing it.
MBL on the other hand, makes it harder for people to discuss their ideas if they do things that people disagree with. I understand that maybe it's the only way to have their voice heard, i don't think it is, it's just that change in public consciousness happens slowly. It still is better than nothing i would say, but doing things that will make people angry is not the best way to get them to listen to you.