It's one thing to express concern for good cops being killed or injured in the line of duty, but another to express it using a form of words which suggests it's a retort or response to BLM. The implication of sloganizing it that way in this context is that cops are dying because of an excessive level of concern for the lives of black people. Which is both offensive and just not true. Cops die because the US is a violent society (with a lot of weaponry). If one wants to express concern about that, a different way of expressing it might be less divisive.
Black Lives Matter as a slogan was intended to relate to a specific issue, which does not have a police equivalent. Police officers are not dying because of institutional and historical prejudicial attitudes against the police.
I would hope that JDM was intending to express the first sentiment, and didn't think about the implication of that way of expressing it.
This.
They specifically chose Blue Lives Matter in an attempt to refute that there is systemic racism within law enforcement. It really is as simple as that. They knew exactly what they were doing and why they were doing it when they came up with that name.
And yes, this stuff can serve as dog whistles, because it is clearly focused on people that want to push that narrative, while seeming innocent to average person that isn't aware of the situation.
Lots of "alt-right" (or rather radical right) groups and personalities have openly admitted that they've been seeding dog-whistle terms, because they know that people that know what those actually mean will react (if they're of like mind they will laugh, if they're not of like mind they'll get rightly pissed off), while the average person will be ignorant and will propagate it, thinking its going along with something similar (the "___ lives matter"), or is just random nonsense (i.e. the Pepe memes) done as harmless fun. Which is why you get "moderates" buying into the "too PC!" bullshit because they're either ignorant or don't want to believe that such hate groups/people can hijack pop culture to spread their beliefs. There's more (i.e., take the "objectivists" like that Google person that wrote the one memo, where they're pretty much just pushing old school eugenics beliefs)
Just like how the KKK knew to go after disenfranchised soldiers that left the military, these groups are keen at targeting certain "at risk" groups. Lots of cops feel victimized by the revelations, so they latch on. And the "alt-right" knew to target angsty young people that tended to be isolated/introverted/etc. They knew especially to target younger white males and tap into their latent rage (as a white male, and growing up with lots of others, I know it very well, and have come to see how bullshit it is and how it makes us incredibly manipulative).
Its literally the exact same shit that ISIS does (only ISIS targets a slightly different demographic). They use memes and social media to connect, then prod, and when finding someone in the right mindset, then work to manipulate them and win them over to their line of thinking.