Well, I wasn't there, so I'm obviously not in a position to say whether the black woman was being insensitive, but I don't think supporting BLM or civil rights is in opposition to telling a black woman that she's being insensitive.
Black people shouldn't be immune from criticism if their behaviour deserves criticism. That's what true equality looks like.
Given your description, I suspect that this white woman wasn't exactly measured or reasonable in her criticism😅. But yeah, I don't think it's hypocritical for a BLM supporter to criticise a black woman about how she talks about trans people.
But yes, it's fascinating how many people don't see "not watching the special" as a viable option if they find it offensive. Though, of course, the fact that many of the people criticising it haven't watched it is probably what's causing most of the outcry.