I understand that many people believe Black Lives Matter is just a statement and by saying it, they are supporting injustice and the fight against racism. I doubt many of the people that say they support BLM actually know what they stand for from their own web site. Read it, understand the movement and what they want before you support something. What they believe is decidedly tribal and taking care of their community. Not the community of people in general. It has many of the Marxist messages in their statement as well as not believing in a nuclear family but rather a village to raise the kids.
To say it is not a political organization is wrong. They are organized, they take donations, they influence political candidates through their support or critique, they influence businesses, etc. They are as political as any other super PAC.
If someone wants to support them, that is okay, its their right. If someone say's they believe in them, that is okay too, just know what you are supporting, but it has NO place in schools just as any other political teachings shouldn't be in schools. Every child should be able to develop their own political beliefs on their own without having it being drilled into them from teachers.
To say that this is a fight against systemic racism is also wrong. Systemic would mean that the system is rigged against them, the laws are written to be against them, and they do not get equal treatment under the law. There are of course individuals that are pure racists and need to be dealt with under the law. If anything the system is rigged to help minorities get a leg up. Colleges have quotas that allow for accepting more minorities regardless of how their scores compare to non-minorities. Businesses cannot discriminate against minorities and must have very good reasons for terminating them otherwise the EEOC will step in on their behalf whereas non-minorities do not have any of those protections. Nowhere in the constitution, federal law, state law, or local law, does it disadvantage an ethnicity or race. All US citizens are equal under the law. Anything other would be thrown out by the courts.