There’s nothing stopping anyone for showing support for BLM, if that’s what they want to do, regardless of skin colour. I have problems with some views shared by BLM activists, but I don’t think their aim is to exclude anyone for ethnicity.
The problem with an ‘all lives matter’ approach is that it obscures what the issue is. The issue being black people being unfairly treated in American/European society because of skin colour. White people do not face the same issues of police brutality or racial discrimination as black people do, so making it ‘all lives matter’ would cause it to lose focus. I don’t see the need, as a white person, to feel centred in a movement when I do not face the issues to the same degree as black people.
As for the troll, I am not going to bother engaging.