"the movement."

[Aristocatt]

Again, It sounds as though you are choosing to interpret the statement how you see fit.
From one perspective you suggest they are anti democratic.
From another perspective it seems as though they might be calling for a more perfect Democracy and are asserting that a series of institutional undemocratic barriers causes the black community to be underrepresented in society today.
Or you know maybe, like any activist group, they use the word demand loosely when creating a list of what they would like to see.

So with two/three/more competing ideas about what BLM really wants, we could of course send them an email and ask them to clarify their position. Maybe all of our interpretations are wrong! Or we could look at the rest of the page see what they say they want.

For example they make a series of "demands" about voter registration. Whether or not you think these are good ideas, the issue the are bringing up is specifically that current law disenfranchises their community. These are specifically claims that the current process is undemocratic.
So BLM makes a statement that summarizes their demands that is ambiguously undemocratic.
Then they say they want to improve democracy.
Then they have a series of demands that they explain should be met because if they are not, the democratic process itself is being undermined.

Sounds fishy. I think you are suffering from confirmation bias. You want BLM to be undemocratic so you work to prove, poorly, that they are undemocratic.