You should and can care about black lives. however, this is not a part of your daily life, and should not be taken into consideration during it. Ever come across a group of white supremacist harassing a black person? Or say a black child in danger from a vicious dog? These are scenarios where you might be forced to make a decision. When their lives may depend on you. You may even need to come to the defense of a black co worker, this of course should not be based on skin color, but of simply doing the right thing. Or so to say, the color of their skin should not effect your decision either way.

Now if you think the current movement is bogus propaganda for political reasons, and are against rioting and looting, you can openly oppose the Black Lives Matters movement. Many black people are opposing it. After all it's clear that the people looting their grocery stores don't have their best interest in heart. This is creating a negative image that they do not wish to be associated with, one no better than the KKK.

Fortunately, or unfortunately, the best thing to do, is to simply go about your life. That is unless their is actual rioting going on outside your front window. In which case.... Keep your drapes closed and put a lock on your gate.