This may be a case where getting it wrong twice gets it right.
Intended abstract nugget of wisdom: "If you want to think or act rationally, don't act like the caricatures on television that do things less effective than the people they are contrasted with. Just do the effective things."
Simple description of what the meme means: "Being rational does not mean being like Vulcans from Star Trek."
Mistake 1: Vulcans don't usually act like that which the meme would condemn either. The description doesn't match the intended message.
Name of meme: "Straw Vulcan [Rationality]"
Mistake 2: If you use "Straw X" in approximately the same way as in "Straw Man" then the wording of the meme doesn't suggest that the Vulcans are irrational---quite the reverse. This remains true no matter which way you split it: "(Straw Vulcan) Rationality" or "Straw (Vulcan Rationality)".
Both of those suggest that the desired thing (either the Vulcan themselves or their Rationality) has been corrupted by the accused so that it is readily criticised. It means "Don't be like fake depictions of Vulcans, be like actual rational Vulcans".
If we assuming Brienne's positive depiction then Straw Vulcan Rationality is close to perfect terminology to be using, so is the fundamental lesson. It's that intermediate description that needs to go. Because relying on making two mistakes in order to get it right is a bad habit to get in to!
There's a core meme of rationalism that I think is fundamentally off-base. It's been bothering me for a long time — over a year now. It hasn't been easy for me, living this double life, pretending to be OK with propagating an instrumentally expedient idea that I know has no epistemic grounding. So I need to get this off my chest now: Our established terminology is not consistent with an evidence-based view of the Star Trek canon.
According to TVtropes, a straw Vulcan is a character used to show that emotion is better than logic. I think a lot of people take "straw Vulcan rationality" it to mean something like, "Being rational does not mean being like Vulcans from Star Trek."
This is not fair to Vulcans from Star Trek.
Central to the character of Spock — and something that it's easy to miss if you haven't seen every single episode and/or read a fair amount of fan fiction — is that he's being a Vulcan all wrong. He's half human, you see, and he's really insecure about that, because all the other kids made fun of him for it when he was growing up on Vulcan. He's spent most of his life resenting his human half, trying to prove to everyone (especially his father) that he's Vulcaner Than Thou. When the Vulcan Science Academy worried that his human mother might be an obstacle, it was the last straw for Spock. He jumped ship and joined Starfleet. Against his father's wishes.
Spock is a mess of poorly handled emotional turmoil. It makes him cold and volatile.
Real Vulcans aren't like that. They have stronger and more violent emotions than humans, so they've learned to master them out of necessity. Before the Vulcan Reformation, they were a collection of warring tribes who nearly tore their planet apart. Now, Vulcans understand emotions and are no longer at their mercy. Not when they apply their craft successfully, anyway. In the words of the prophet Surak, who created these cognitive disciplines with the purpose of saving Vulcan from certain doom, "To gain mastery over the emotions, one must first embrace the many Guises of the Mind."
Successful application of Vulcan philosophy looks positively CFARian.
There is a ritual called "kolinahr" whose purpose is to completely rid oneself of emotion, but it was not developed by Surak, nor, to my knowledge, was it endorsed by him. It's an extreme religious practice, and I think the wisest Vulcans would consider it misguided1. Spock attempted kolinahr when he believed Kirk had died, which I take to be a great departure from cthia (the Vulcan Way) — not because he ultimately failed to complete the ritual2, but because he tried to smash his problems with a hammer rather than applying his training to sort things out skillfully. If there ever were such a thing as a right time for kolinahr, that would not have been it.
So Spock is both a straw Vulcan and a straw man of Vulcans. Steel Vulcans are extremely powerful rationalists. Basically, Surak is what happens when science fiction authors try to invent Eliezer Yudkowsky without having met him.
1) I admit that I notice I'm a little confused about this. Sarek, Spock's father and a highly influential diplomat, studied for a time with the Acolytes of Gol, who are the masters of kolinahr. If I've ever known what came of that, I've forgotten. I'm not sure whether that's canon, though.
2) "Sorry to meditate and run, but I've gotta go mind-meld with this giant space crystal thing. ...It's complicated."