it turns me away from it as a serious movement I could support.
As I said, you can still support their cause - regardless of what you believe about the Marxist roots of the movement. I can tell there is no persuading you away from your notion they are related to Marxism - or that this is not really a problem if true. I can't say that just because you disagreed with some things in the sixties, means that the people today are the same, using the same techniques in the same way - even as they are using some of the techniques that have proven peaceful and effective.
No more than I can use similar methods to point out that you are using the tactics an language of those that have historically retarded civil rights movements, trying to shift focus away from the problems - and the call to action and instead trying to look at a small number of cases, and to use loose associations to try to build a shoddy, but persuasive to some, case of guilt by association.
If you acknowledge there is a problem that faces black, and you work towards fixing it - that's the main thing. If you agree that black lives matter, and the system is presently treating them as less you should be supporting their cause. Forget 'supporting the movement' because it isn't a singular entity. There are no doubt raging Marxist revolutionaries amongst them - and perhaps these are the kinds of people that become spokespeople and organisers in these movements. There are millions who support their goals that are none of these things. Support their goals, stop shitting on things for dubious reasons.
If you can support '#DefeatHitler' even though major players in the movement were literally run by Stalin - you should be able to support a cause like #BlackLivesMatter even if some members believe civil rights issues are a struggle between two groups of disparate power (ie., what you seem to be calling Marxism).