So the BLMGN who owns that website, isn't representative of the movement, it is one group who is using the name of the movement.
So you really shouldn't ready anything into what is on that site as to being representative of the BLM movement.
I mean, I know that, and on one level you are right (trivially so), and on another level I think you're missing the forest for the trees. Granting that this is a side tangent I won't dwell on it and just posted as food for thought. But the No True Scotsman/shifting goalpost should certainly be clear to you as present in movements like these. As long as there is no central authority (which is usually the case in human affairs, especially grassroots ones) then any claim at all can be said to "not be representative" of "the movement". So basically no claim made by anyone can be held to account, since it's not 'the official' belief, since there is no official belief. So we can't say anything about anything under this principle. I assume you would find this as odious as I do if it was being made by groups you found troublesome, and their defenders making motte/bailey 'that's not what people really believe' arguments. I'm not precisely saying you're an apologist for BLM - although in this instance you literally are - but rather than one can go too far being fair to them rather than finally admitting that some things really mean what they sound like.
This is the problem with protest and political movements: you want a coalition, and to claim solidarity in numbers, but when critiques are leveled, everyone goes to ground and claims it was someone else's belief, not theirs. So to have your coalition you knowingly thumbs-up any statement made at all ostensibly on 'your side'. So for an example, in the trans movement (just to throw fuel into the fire) you will rarely see pro-trans activists taking each other to task for statements they disagree with. Rather, you'll see a lot of support for those on support of the same side, even if their beliefs are in fact different or even contradictory (which happens quite often). This works for them so long as this coalition creates a large public presence, but as I mentioned results in no one being accountable when problematic claims are made.
So I know that not literally every left-wing person wanted to literally abolish the police. But I was referring to this claim made that, 'no, we don't actually mean that, that's just a smear tactic.' Well I'm saying it's not a smear tactic, and that it was a real proposition most likely fueling the riots. I don't think the people occupying city blocks were protesting the precise budget levels of the police, preferring they be somewhat lower. And by the way, contrary to public opinion, most people are not particularly subtle, and are not either trained or at least required to come up with more complicated thoughts than "down with X!" Maybe they can, but why should they bother?
I'll just throw in as a bonus that I'm not even address what I think about the idea of abolishing the police such as they are now! My opinion on this might surprise you. But mostly I'm addressing the dismissal that this is what the maxim means, at least in many contexts.