As a movement, BLM has seen fit to address all kinds of things that go way beyond the narrow scope you're suggesting. last year, they helped take over various college campuses, where they intimidated reporters, threatened students, and have since shut down public speakers at universities.
None of those have anything at all to do with police violence.
So is it OK for BLM to interfere on anything they feel entitled to interfere on, but if we are trying to criticize them we can only do so about their alleged mission statement and nothing else?
Incidentally, they destroyed much of Milwaukee, not over some unarmed ten-year-old or something like that but over a very-armed known criminal. So there, police were doing their basic jobs, and BLM still called for massive riots and violence.