All lives do matter--but sometimes it's very important to focus on particular lives at risk.
In this case, though, my point is that the issues pull in all directions. There is not, for the reasons I outlined, a particular synergy between these two groups. What is uncomfortable is not at a personal level but that the group-level interests don't perfectly align on average. But there is still human solidarity in general, and individuals can of course befriend each other for a variety of reasons.
(I know about the origins of BLM, but these days it's mostly focused on police violence, hence my comment.)