It's not the same, though, is it? If someone is killed by police inside a building with nobody pointing their phone, and police body camera footage is not released, the police narrative of events stands. When something happens in a public space and a bystander captures and uploads moving images and the police narrative doesn't match, all hell breaks loose, regardless of the race of police or victim.
Unless you think people in the streets are ignoring whit victims of police violence, you have to look at the statistics and conclude that not only are black people killed by police at a rate x3 to white people per 1000000 of population, but police feel they enjoy much greater impunity to kill black people in full view of passersby.
Regardless of all the above, if police are starting to be held to account, their funding reviewed, their training upgraded and their ranks pruned of the unstable and trigger-happy, won't white people benefit as much or more than black people?
BLM means BLM too. It doesn't mean only BLM.
White parents don't routinely feel the need to educate their sons and daughters in how to survive an encounter with the police. Perhaps they should, but they don't. If police officers begin to be taught how to de-escalate tense situations instead of inflaming them, I can only see benefits for all.
I can't see any reason why everyone wouldn't be in accord with the aims of BLM.