Just because a belief is the product of irrational cognitive processes doesn’t mean that a logical argument can convince the holder of that belief to abandon it.So your analysis doesn't explain why those folks who may have initially sided with Picard's decision still do so even after long debates about the illogic and implications of such a position. It seems going by what you say, we should be expecting to see them reevaluate their positions AWAY from the immediate emotional impact of the film.
We like to think of ourselves as logical beings, but there are many cognitive processes in our heads that are not logical and of which the conscious mind may not be aware. I suspect that beliefs not born of logic are less susceptible to logical argument than than beliefs born of faulty logic. If something doesn’t rest on logic in the first place, you can’t knock it down just by kicking the logic out from under it.
(This might make an interesting way in some cases to test the origin of a belief. Suppose somebody argues a position from faulty logic, and you clearly point out the flaws in the logic. If he goes, “Oh yeah, you’re right,” then the faulty logic was probably the source of the belief, and when the flaw in the logic became apparent the belief was abandoned. If he stubbornly clings to the position, then the faulty logic may be a rationalization of a belief to which he’s committed for other reasons.)
It seems to me that most of those who defend the film are not accepting the film on its own merits.Yet people who side with the "anti-removal" position still do so in a context totally removed from the film. I can only conclude from this, baffling as such a conclusion might appear to you and me, that they really DO support this position, it's not a feature of the immediate impact of watching Picard and company on film.
The moral position staked out by the film isn’t subtle or ambiguous. The planet is the Ba’ku’s home, they have a legitimate claim to it, and they have the right to continue to live there free from outside interference. This right outweighs the public health benefits of the particles and the chain of command.
Some may actually agree with that position, but for the most part we see people defend the film by claiming that the moral issues presented in the film aren’t really what the previous paragraph describes. We get claims that the battle is really about honesty, that the particles wouldn’t really have the benefits Dougherty describes, etc.