That's honestly just an interpretation of it. He could just mean "remember this day of protest against the establishment". Everyone just reads everything he says with their own biases.

I don't think that's inherently wrong, just let's not ban people based on our own biases.

All of the intepretations of the events that happened yesterday could be equally uncharitably interpreted of BLM with the riots, violence, and protests across the country. I mean, they forcefully took over an entire city zone at one point.

Well that is the cleverness of most trump statements, toe the line, give a nod to your side, but also retain deniability. If you don't start interpreting, you get into a trap in which you will be outfoxed by anyone who can toe lines enough to not blatantly incriminate themselves.

As for BLM, personally I was never very sympathetic to the portions of protests/riots that caused violence.

Dog whistles work because they proved the fig leaf of plausible deniability. Trump's presidency has been a series of dog whistles. Why would it have stopped just because he lost an election?