Arational quotes

the function of the repetition of these quotes down the years has been to signal tribal affiliation.

Affiliation with the tribe against Reagan and Bush, right?

I offer the hypothesis that the function of the repetition of these quotes down the years has been to signal tribal affiliation.

Your hypothesis seems clearly true to me, and I have thought of it myself. However, with these quotes, I was really unable to figure out which exact bad-faith misinterpretation was being suggested. (Admittedly, as I note in my response to Joshua Z., my own original interpretation of the Bush quote may have been too favorable, though even in that case, it still requires a hostile over-stretching to make the quote a remarkable exhibit of irrationality.)

Hm... it is possible that my English comprehension has failed me.

I interpreted the phrase "which way the wind is blowing" to mean the prevailing fashion and majority opinion, so that the quote would contrast making decisions based on principled conviction with bowing down to momentary fashion and popular pressure. (This phrase, i.e. its literal translation, is commonly used in this sense in my native language.) However, looking it up, now I see that this is not its usual meaning in English, though such meaning is attested to some degree.

So the question is, did Bush actually use the phrase "which way the wind is blowing" with this somewhat unusual meaning? It's hard for me to tell. (Even if this meaning is unusual or archaic, I can think of at least one other occasion when Bush was derided by many people for using what they thought was a bizarrely incorrect word, but the joke was in fact on them and their ignorance, since the word is nowadays unusual and archaic, but perfectly standard and well-attested. I have in mind the occasion when he referred to "Grecians.")

In any case, even if Bush didn't have this meaning in mind, the quote can be interpreted as making the assertion that in matters of politics firm and consistent principles provide a better guide for action than frantic and futile attempts to analyze each particular situation better than is actually possible, which leads to overthinking and indecisiveness. Whether or not one agrees with this, it's certainly not something deserving of being included into a chrestomathy of human irrationality.

you need to take into account background knowledge about George W. Bush (such as that he is a person who believes that God talks to him.)

Oh good lord, this whole topic so far is two quotes from Republican Presidents, and the supposed irrationality of the quotes seems to be nothing more than strained readings of what they meant. Can people come up with any examples of irrational/arational quotes that aren't just a labored attempt to ridicule the chieftain of the enemy tribe as a form of tribal affiliation signaling?

But this is implied in the quote.

You're giving the quote a bizarre and implausible reading. Of course that Reagan (if he really said this) meant it to imply that a marine does make a difference, and a positive one. Any normal person interpreting the quote in good faith would make that assumption, whether or not they agree with the premise.

(Besides, googling for the source of this quote, I can't find any reference to a concrete time and place where it was uttered, nor to the rest of the speech or dialog whose part it was. This strongly suggests that it might be apocryphal, though of course I can't conclude this with certainty.)

If the quote instead concluded with "The Marines verifiably know they do make a difference."

Then it would say the same thing but say it poorly. That this ending even occurred to you as you read the quote should be treated as evidence that this is what was meant. It is a common and highly effective rhetorical technique to leave a key element implied rather than explicitly stated. Stating it explicitly undermines the rhetorical impact. We might compare it to explaining a joke, which kills the joke.

But as it stands the quote just says the Marines no longer wonder about this, and presents it for a good thing.

You're misreading the quote by assuming that it did not leave a key element implied.

I was thinking that it could be interpreted as the Marines knowing they don't make a difference. It reminds me of this quote:

Dr. Nefarious: "To think, they called me insane, Lawrence. We'll see who's insane when my [mutant armies] have exterminated all life on this miserable planet!"

Lawrence: "That should clear things right up, sir."

To generalize, that quote is part of the same philosophy that thinks faith better than agnosticism, belief better than unbelief, certainty better than uncertainty -- regardless of whether the evidence justifies such or not.