When BLM is mentioned, I often see people criticize their methods, the underlying ideology of some members and their claims to truth. I have never seen anyone not care about black people being killed.

There is, of course, a possibility that I'm living in an opaque filter bubble and that the racist hordes are just outside. If I am, please pop that bubble and show me the truth.

To be fair to ACLU, they have good record defending speech no matter who talk. The did care about civil rights groups speech as much as KKK.