I have heard people relate or describe Black Lives Matter as described in Luke 15:
Now the tax collectors and sinners were all gathering around to hear Jesus. But the Pharisees and the teachers of the law muttered, “This man welcomes sinners and eats with them.” Then Jesus told them this parable: “Suppose one of you has a hundred sheep and loses one of them. Doesn’t he leave the ninety-nine in the open country and go after the lost sheep until he finds it? And when he finds it, he joyfully puts it on his shoulders and goes home. Then he calls his friends and neighbors together and says, ‘Rejoice with me; I have found my lost sheep.’ I tell you that in the same way there will be more rejoicing in heaven over one sinner who repents than over ninety-nine righteous persons who do not need to repent.
Do you think this is similar to the message of Black Lives Matter? When 100 sheep go missing, Jesus leaves the 99 and goes looking for the 1. The other sheep wonder, "don't we matter" which is similar to All Lives Matter. Of course the other sheep matter, but they're not the ones in danger so they are not the ones Jesus is paying attention to.
Unless you believe there is no history of racism in this country with lingering impacts, or that black people do not have any inherent disadvantages or discrimination due to skin color, I could see how one would relate the passages.
Directly after this passage follows the Parable of the Lost Coin and the Parable of the Prodigal Son. They reflect the importance of redemption and asking forgiveness. They analogize persons who are lost souls, and the significance and joy of them finding their way through God's grace. It is specifically the sinners or non-believers that need God most, so there is special attention paid to those people despite being less than ideal models of God.
I'm not saying black people are lost souls, but what do these passages mean to you in relation to the BLM movement, or having compassion for people who do not glorify God or live by His example? The Bible is filled with stories about empathy, compassion and forgiveness even for those who are not worthy. The lesson is to exemplify God's grace to others, and by doing so you and them can be saved. How can we be more Christian in our politics or social politics to live by God's word?