First of all, let’s tackle the question in the thread topic:
Suppose that one answers “no” to the question. What does one propose should be done as a result?
When I see a flashing blue/red light in my rear view mirror, I pull over as required by law. When I do so, I assume that I’m going to be treated relatively courteously, and professionally, by an officer who will comply with the requirements of the Constitution and the relevant state laws in interacting with me. I do this despite the fact that on more than one occasion, officers who have pulled me over didn’t do that (thank-you, Kansas). I do this because the alternative options aren’t very good. What should I do if I [don’t trust that things will go well? Not pull over? Bad. Not interact with the officer? Bad. Get belligerent with the officer, and challenge what I think is wrong? Bad.
People who are interacting with officers of the law in these situations are not at their best, obviously. It’s stressful. It’s also stressful for the officer. But you have two basic choices: comply with the officer’s requests or refuse to comply (maybe doing something else instead). If you comply, you might still have your rights abused; some officers do bad things. But if you don’t comply, you almost definitely will have something happen that you won’t like, because failing to comply is going to get a reaction from the officer in order to obtain compliance. So anyone who tells someone that they shouldn’t comply with the request of an officer (unless that request is clearly illegal) is not giving good advice.
So what do we mean by “trust” the police? If by “trust the police” we mean believe that the police will do the right thing, then I think that’s going to be up to the person and their experience. But if by “trust the police” you mean “act in compliance of their requests when you interact with them”, I think the answer to that is, yes, you should “trust the police.”
But the OP was really raising a different question. The OP is asking America as a whole when it intends to address these issues in a systemic way. Because, the OP says, to fail to do so will result in a large segment of our society refusing to treat officers of the law with the necessary respect for an orderly society.
As to that, I can only say that, so long as we maintain an “us against them” mentality about things, it’s not going to happen. Complaining about what some officers do is not an attack on all police, any more than the fact that some officers do bad things is an indication all police are bad. I’ve never understood why it is that people who want to defend police cannot accept that police organizations might need to re-think how they handle their interactions with minorities in this country. It’s not going to make things worse for the police who do things the right way, after all. And those officers might end up having a much more enjoyable job once they get to interact with a community that trusts and supports them as a whole.