People who object to Black Lives Matter understand Blue Lives Matter perfectly. The name is not the problem and never has been.
Purely from a linguistic and communications/marketing perspective the name "black lives matter" is potent because it brings up an emotion but the nature of its structure is divisive because the name implies exclusion or inclusion unless you understand enough behind the name. Obviously BLM is not a "product" per se, but from a purely marketing standpoint, when you need to educate "consumers" (mind share of a large group of white folk) for clarification or any other aspect your go against the natural ebb & flow of the brains preferred method of processing (least resistance)
Think of it this way, fuck the name all lives matter. But if you saw a something conveying various messages for multiple shootings of black people by cops with the phrase "we matter" ...multiple times, etc. I think you get a different effect. Heck if I was advising BLM I would produce videos along those lines targeting white demographics simply to convey the core idea behind BLM. I lived the first 25+ years of my life in brooklyn, spent the last couple years here in new hampshire. Seeing black folk here outside of a few areas is not common. You have a large amount of people who are genuinely good people, not racist, but you bring BLM in to the convo and you can see from their body language how uneasy they get. Its ruff. Genuine lack of exposure and ignorance.
Words are powerful thing. You can dismiss them or be pissed off because its not right that some people who are not racist per se just ill informed dont get BLM or get the wrong emotions stirred up. It is what is. Those who study communications or use it heavily to make a living understand that the burden of understanding is not on the listener but on the speaker. If your not getting me, its my fault not yours...