Can one agree that black lives matter, without being a white supremacist: yes. (good so far)
...without needing to support the tactics of the "BLM organization"?
The presupposition that BLM is a single, organized monolith begins to wander into the grey area. Local orgs spring up. Most often, this goes unreported on. When the white+neoliberal news organizations find a "BLM group" that does something they can skew, THAT one gets all the media coverage.