"the movement."

[Aristocatt]

Let's take this one step at a time.
Why do you think BLM is obviously anti-democratic?
"We envision a remaking of the current U.S. political system in order to create a real democracy" - Website you linked.

Click on political power tab and you get this:

We demand independent Black political power and Black self-determination in all areas of society. We envision a remaking of the current U.S. political system in order to create a real democracy where Black people and all marginalized people can effectively exercise full political power.

See what happens when you put things back into context???

The term "real democracy" surplants the current system as it would insure: "independent Black political power and Black self-determination in all areas of society." even if a given community would not normally democratically elect to have an 'independent black political power structure.'

Doesn't seem anti-Democratic to want more representation.
Seems like your just jumping the gun.
So now read the whole page up and down.  
Re-contextualize what you just said and point to a specific anti-democratic policy.
Part of their argument on that page for having more political power(and where they most clearly express what you seem to think is anti-democratic) is that they are not being represented as much as they should be if America was a porperly functioning Democracy.  That's debatable sure, but their general point, if I understand correctly, is just that they want representation that they think they would have if Money/Gerrymandering/Institutional Racism were not there to distort the Democratic process.

The demands BLM makes in order to destroy Democracy:
An end to the criminalization of Black political activity including the immediate release of all political prisoners and an end to the repression of political parties.
Public financing of elections and the end of money controlling politics through ending super PACs and unchecked corporate donations.
Election protection, electoral expansion and the right to vote for all people including: full access, guarantees, and protections of the right to vote for all people through universal voter registration, automatic voter registration, pre-registration for 16-year-olds, same day voter registration, voting day holidays, Online Voter Registration (OVR), enfranchisement of formerly and presently incarcerated people, local and state resident voting for undocumented people, and a ban on any disenfranchisement laws.
Full access to technology including net neutrality and universal access to the internet without discrimination and full representation for all.
Protection and increased funding for Black institutions including Historically Black Colleges and Universities (HBCU’s), Black media and cultural, political and social formations.