It's funny you say that, because from what I see is that the people behind BLM aren't that interested in black lives, they are more interested in bringing about their socialist/communist utopia, disrupting the nuclear family, and replacing American and religious culture with their own agenda. I'm sure some will disagree with that, but that's where the politics comes in. BLM also funnels money to the Democratic party, so supporting them is supporting the Democratic party. Why should a sports league be involved with supporting one of the nation's political parties?
Everyone, or nearly everyone, is for justice and equality, but it isn't that simple. What constitutes justice? Should every cop who has shot a minority in the past 10 years be imprisoned, no matter what the circumstances are? Should the police be defunded? BLM says so, but the majority of Americans do not. What constitutes equality? Quotas? Reparations? Diverting funds to the inner city? Teaching children that the US was not founded in 1619, not 1776? Removing the 4th of July as a holiday because it celebrates white supremacy (as Colin Kaepernick claimed)? These are complicated issues, it's not as simple as saying hey we believe in equality so let's paint the name of a political organization on the court.