The things you listed don't really have another side in that anyone relevant would take. Who doesn't want a cure to cancer or would love for kids to drop out of school to join gangs? Those have little to no political sides drawn.
Does racial injustice or should it? No.
But the specific cases used as examples people do have a problem with. And the supposed discussion is not a discussion when specifically talking about police injustice because discussing behaviors that in many instances (not all) could have resulted in no one being killed can't be discussed because that is then looked at as justifying the police officer's bad actions in handling the situation. When in many of these cases while the police officer is more wrong than the victim, there are learning opportunities not discussed on not resisting and taking legal recourse if need be for an illegal arrest. But if someone was to try to mention that or discuss that, they would immediately be shouted down saying resisting arrest should not be a death sentence or that is justifying the police officers bad actions. And that isn't necessarily the case. The discussion can be what are different actions each party could have taken to have prevented the result of death. And yes the police officer in the valid examples are much more at fault and shouldn't have done what they did, but isn't the goal to prevent the death in the future in similar interactions?
I don't disagree with the premise of your argument, but I think it's overly analytical. The bottom line is the issue of race is still sensitive in America. Hence the visceral reaction to it. The expression "Black Lives Matter" should not engender such a visceral response from people, but obviously it does. And it's not for the principled reasons people like to think. It's because people don't like to face things that make them uncomfortable.
Breast cancer awareness has no history of prejudice, culturally or institutionally, so that's why you won't hear anyone say, "All cancers matter," or any dude say, "What, my testicles aren't important?" during pink ribbon month. The same as you won't hear people say, "Yeah, but the NEA is a Marxist organization and there are some pervy high school teachers," when the NBA promotes high school graduation.
Discussing racism makes people uncomfortable for a reason. For many, it's as simple as they are being asked to confront their own biases and prejudices, whether they be implicit or pronounced. Supporting law enforcement and believing black lives should be regarded equally do not have to be opposing values anymore than someone has to agree with teachers unions or accept sexual exploitation in high schools to value public education. For some reason, though, because our society is so tribal and polarizing now, many have developed this attitude that everything "political" has to be an either/or proposition, and that is just not the case. I can support that racism is wrong while also believing law enforcement is good and that suspects should comply with police officers putting them under arrest. The same as I can support that no person placed under arrest, regardless of sins, should have a knee to their throat for almost nine minutes while also believing that a police officer can and should use lethal force when warranted.
It's really not that complicated. Racism is wrong. If that's controversial or too traumatizing to some, then they need to indeed change the channel and find a new hobby.