You can't claim intellectual property rights on lexical elements already in common use. Otherwise, you could copyright "the" and collect ALL THE ROYALTIES.
I can't claim intellectual property rights on my first or last name. I could try on my first and last together. But that is already an associated property within the Screen Actors Guild (not what you generally consider IP, but a protection nonetheless).
That doesn't mean I can't use my name. That doesn't even mean I can't use my name as a public asset, even for acting. It does mean I can't use my name to appear, leverage, or interfere with the work of the actress (I have an androgynous first name) who has already registered it where the SAG can enforce its registry.
The organization BLM might have challenges registering a trademark on the name of a copyright on the phrase. So it might be difficult to monetize the lexeme. (I have seen no indication that they are interested in that.) However, they still have protection against intentional abuse of BLM to reflect poorly on the organization. Libel, harassment, and slander are not traditionally thought of as part of the IP domain, however they are grounded in the same concept of the protection of a created non-materiel work.
While most of the written laws trace back to the 1600's or 1700's in Europe, the ideas have been around for a long time.