Honestly, I wonder how much of our disagreements do ultimately come down to moral philosophy. I see a lot of people making this comparison and I'd be happy to put aside the present political situation and step back to discuss a higher level of disagreement.
I am a consequentialist, and I would agree, in principle, that the correct decision in the trolley problem is to pull the lever. But that should always come with an extreme amount of disclaimers. There are no shortage of people throughout history who have made justifications for their actions on the basis of "the ends justify the means," but often, they turned out to be wrong. To use an example, torture under the Bush administration was claimed to be justified on the basis of getting useful intelligence in order to save lives. But no such intelligence was ever extracted. Really, it was more motivated by revenge, or a desire to be the sort of cool antihero who does the stuff nobody else will that needs to be done, but "the ends justify the means" served as a rationalization. Another example like that (though perhaps more controversial) is the bombing of Hiroshima and Nagasaki.
The problem with applying the trolley problem to real life is that we are mere human beings of flesh and blood. We have a whole host of cognitive biases that mislead us even when we have the best of intentions. If we give our minds a way to justify things that we know are bad, it gives it an out that allows us to rationalize the irrational and justify the unjustifiable.
There are two practices that are necessary to apply in order to counteract these biases. First, it is necessary to adopt a set of strong moral guidelines based on past experience and historical evidence. Second, it is necessary to regularly practice some form of introspection or meditation in order to better understand where your thoughts and feelings arise from, and how they flow through your mind. Said guidelines do not have to be rigorously adhered to 100% of the time, but they should be respected, and only deviated from after clear, careful consideration, understanding why the guideline exists and why deviation from them is almost always bad.
"Base" consequentialism, where you recognize that pulling the lever in the trolley problem is the correct decision, but simply accept that as a guiding principle, is a terrible moral philosophy, worse than deontology and possibly worse than having completely unexamined moral views. Some of the worst atrocities in history are the result of that sort of "ends justify the means" approach, detached from a set of moral guidelines and detached from humility and self-reflection. I would even say, speaking as a communist, that many of the bad things communists have done in history are a result of that kind of mentality. Following moral rules blindly is preferable to breaking moral rules without first doing the necessary work to be trusted with breaking them.
There's plenty more I could say on the topic but people always complain about my long posts so I'd better cut myself off there.