The American right wing consistently makes the worst argument in favor of their policies and police. They should have promoted the good stuff police do and not have had such a confrontational stance with the protest. And Blue Lives Matter people definitely need to distance themselves from Confederate and Trump defense.
I think the arguments you pick to defend certain policies say a lot more about where you are coming from more than the stuff you pick and choose to like. Especially since very few people develop comprehensive and consistent political identities. The fact that police supporters chose to take a stand when it comes to monuments and black urban crime discredits the whole thing. If that is how they really feel then we should defund the police and rebuild the system from the ground up.