I think that trolley problems contain perfect information about outcomes in advance of them happening, ignore secondary effects, ignore human nature, and give artificially false constraints. Do you agree with that part?

"false constratins" carries a negative connotation. Here you setup your emotional argument later. This site is about rationality and you made a mistake here. Even if it is understandable and common human thinking it is that which is "sloppy thinking". Otherwise this premise is more or less correct.

Now, I think that's bad. Agree/disagree there?

Disagree. With the same argument you could say that animal testing is bad because it doesn't recognize the differences between humans and animals. The point is, it does. As long as you know the limits of the results of animal testing, they still serve as a pointer towards how humans will react to substances. And as long as you are aware that trolley problems are not real life problems they still serve as a pointer towards what a rational morality needs to answer.

Okay, finally, I think this kind of thinking seeps over into politics, and it's likewise bad there. Agree/disagree?

Except for the likewise. If people make choices based on thought experiments without thinking about whether they really apply, that is bad. But you have only shown how people could do that and not that they actually do. If your post was meant as a general warning against mindlessly reducing real life situations to thought experiments it would be a valid point, however the structure of your post doesn't make that point clear.