I think the meaning is, that on reading something unpalatable, one may be tempted to write it off as "crazy" or "stupid" quickly, and then ignore it, and trying to see the good in it may be more useful; and calling the writer crazy or stupid will make further communication more difficult. So when someone uses those words too readily, that person is called "mean", and seen as not "nice".

"cleverness" comes to mind as a better substitute

Or "Hubris". In the examples, the people go wrong not because they are using reason and they should not use reason, but because they falsely imagine they are capable of using reason sufficiently to deal with the particular issue.

Deism in the 17th century was a move towards rationalism, away from the idea of a God who interfered in the world. Rationalists now will not be deists, but deists during the Enlightenment were more rational than society in general, and were moving towards atheism. I suggest that you use the word "atheists" rather than "non-deists" in the title.

A rewrite, using Feeling words: if you feel happy, content and fulfilled, you will be better able to do the things you have to do. If you believe that doing those things is likely to accomplish a goal you have, you will be better able to motivate yourself to do them. If you cannot bring yourself to do what you have to do, find something which will make you feel happy, content or fulfilled; or if you cannot do that, play Tetris or whatever which will at least take your mind off the guilt, until it comes back worse later.

What will make you feel fulfilled? What will make you feel that doing the task you have to do will make achieving your goal more likely?

When I tried this technique, I did it very slowly. It was like asking whether a word to write felt right. Then I did a drawing which seemed to contradict what I had been thinking consciously shortly before.

I am not aware of research on the technique.

Edit: major plot spoiler in this comment.

You miss out a major point of the story, that those who agree to sacrifice others' children are dishonourable, and that this matters; and that the main character, who sacrifices only one child to save all the rest (his grandchild) suffers terribly for this.

I would not argue from fictional evidence, but the storytellers seem keen to point this out. Also, when deciding to sacrifice children, all possible other courses of action must be eliminated first.

Edit: for me, the main interest of the trolley problem is the emotional response. Would you kill one to save five, if saving the five was certain if you killed the one, and impossible otherwise? Er, yes, I hope so, though I think such a situation, with such certainty, is unlikely. How do you feel about trolley problems generally? Horror and disgust. Then I see that even if I am not going to be in that situation, I may be in situations where I must behave rationally, and Stoically fight down emotional responses.

Among lawyers, this can show high status. Lying to a court is completely unacceptable, and can make an advocate useless to future clients. However NTL is OK.

The pupil barrister: "To be honest..."

Head of Chambers: Lawyers are always honest. The lawyer will say, "To be frank..."

(taken from the BabyBarista blog)

"Now, what I want is, Facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of any service to them" - Mr Gradgrind, Hard Times (Dickens)

An anti-rationalist quote. Dickens believes there is more to life than rationality. Does his satire upon us here have any basis in reality?

Not signalling is

plausibly a more honest mental mode

Why should it be more "honest" not to signal? We are a social species. I conceive it possible to make a close relationship closer by signalling to ones partner what is actually the case.

Things like exercise, studying, which increase fitness and status may be motivated by the desire to increase fitness and status, with signalling only a by-product of this.

In moments of threat where the amygdala takes over, and time seems to slow down, a person responds to the threat, probably without signalling. But it is meaningless to say that I am "honest" when in a fight or flight situation, and at no other time.

I am irritated to find my post named as "nitpicking" when I was answering a direct question. I too "got the meaning and moved on". Alvarojabril below, much clearer- "The glance of a lover will still be alluring". Why not go with that?