This is an interesting perspective, and it is rational. It seems to me that those who proclaim “All lives matter” also feel ignored or demeaned. It does not matter that they are not stopped by police for “driving while white”, they still feel that much of society does not believe that their lives matter. They feel left behind. That’s why the MAGA rhetoric is appealing. It makes many people feel validated.
The lack of empathy that is so rampant in our society is a result of people of all persuasions not feeling valued. What that looks like on the surface is quite different, and we should distinguish the different forms it takes, especially when it involves violence against specific groups of people. Black Lives Matter is a legitimate calling to end racial targeting and institutional discriminatory practices. It does not diminish other groups, but understand that others may feel that it does.