You're not going to persuade anyone by calling them "racist" - a term so abused by motte-and-bailey tactics as to have lost all meaning. If what they say is false, then say so and argue your case.

While BLM can refer to a number of different things, there happens to be a non-profit called "Black Lives Matter", the founders of which explicitly claimed to be trained Marxists.

Whether this organization was rightfully the face of the BLM movement is debatable, but regardless it enjoyed a fair degree of prominence for a time.