The thrust of your argument appears to be that: 1) Trolley problems are idealised 2) Idealisation can be a dark art rhetorical technique in discussion of the real world. 3) Boo trolley problems!

There are a number of issues.

First and foremost, reversed stupidity is not intelligence. Even if you are granted the substance of your criticisms of the activists position, this does not argue per se against trolley problems as dilemmas. The fact that they share features with a "Bad Thing" does not inherently make them bad.

Secondly, the whole point of considering trolley problems is to elucidate human nature and give some measure of training in cognition in stressful edge cases. The observation that humans freeze or behave inconsistently is important. This is why the trolley problems have to be trued in the sense that you object to - if they are not, many humans will avoid thinking about the ethical question being posed. In essence "I don't like your options, give me a more palatable one" is a fully general and utterly useless answer; it must be excluded.

Thirdly, your argument turns on the claim that merely admitting trolley problems as objects of thought somehow makes people more likely to accept dichotomies that "justify tyranny and oppression". This is risible. Even if the dichotomy is a false one, you surely should find one or the other branch preferable. It is perfectly admissible to say:

"I prefer this option (implicitly you presume that will be the taxation), but that if this argument is to be the basis for policy, then there are better alternatives foo, bar, etc., and that various important real world effects have been neglected."

Those familiar with the trolley problems and general philosophical dilemmas are more likely to be aware of the idealisations and voice these concerns cogently if idealisations are used in rhetoric or politics.

Fourthly, in terms of data, I would challenge you to find evidence suggesting that study of trolley problems leads to acceptance of tyranny. I would note (anecdotally) that communities where one can say "trolley problem" without needing to explain further seem to have a higher density of the libertarians and anarchists than the general population.

So in rough summary: 1) Your conclusion does not follow from the argument. 2)Trolley problems are idealised because if they aren't humans evade rather than engage. 3) Noting and calling out dark arts rhetoric is roughly orthogonal to thinking about trolley problems (conditional on thinking). 4) Citation needed wrt. increased tyranny in those who consider trolley problems.