Have you considered the possibility that a lot of people agree that action should be taken, and that statistically-speaking, that positive action will reduce unnecessary deaths for all people, regardless of their race or ethnicity?
If a software bug is reported to affect a certain subset of users more often than others, but upon investigation, it turns out the bug is a duplicate of another more fundamental bug that affects all users relatively equally, are we preventing action (or discrediting that subset of users who reported the bug) by marking it as a duplicate and giving priority to the fundamental issue so as to fix it for everyone?
Just as Black Lives Matter supporters often claim that the phrase is misunderstood by those who question it, All Lives Matter is misunderstood by many who think it takes something away from the black community. It's not a denial of anything, but rather a recognition that the problems actually do statistically affect everyone, and singling out one race (when all are affected) actually does more harm than good when it comes to ending racism.