if you say that X is true for people everywhere, you better show me you did real experiments in different cultures. Also, if you tell me that X is different.
That's very reasonable standard, but I don't think people apply it consistently in this part of concept-space. I agree that people go funny in the head when dealing with personal identity, so one should be more critical of assertions about the universality (or distinctiveness) of a particular identity.
For example, this comment makes an assertion that certain types of effective self-improvement universally have particular properties that some people find undesirable. The universality of that property can (and is) challenged on an empirical basis, but such a possible change was not addressed - or even acknowledged as possible.
Further, sometimes people use your personal-identity-is-the-mindkiller point as a fully general counter-argument to policy positions they don't like.
WEIRD may be weirder than you think. We Aren't The World writes of psychological experiments on non-Westerners that give vastly disparate results from results that have been assumed to be hardwired, and the implications of this:
Henrich used a “game”—along the lines of the famous prisoner’s dilemma—to see whether isolated cultures shared with the West the same basic instinct for fairness. In doing so, Henrich expected to confirm one of the foundational assumptions underlying such experiments, and indeed underpinning the entire fields of economics and psychology: that humans all share the same cognitive machinery—the same evolved rational and psychological hardwiring. The test that Henrich introduced to the Machiguenga was called the ultimatum game.
...
To begin with, the offers from the first player were much lower. In addition, when on the receiving end of the game, the Machiguenga rarely refused even the lowest possible amount. “It just seemed ridiculous to the Machiguenga that you would reject an offer of free money,” says Henrich. “They just didn’t understand why anyone would sacrifice money to punish someone who had the good luck of getting to play the other role in the game.”
...
At the heart of most of that research was the implicit assumption that the results revealed evolved psychological traits common to all humans, never mind that the test subjects were nearly always from the industrialized West.
Edit: The actual papers this article writes about are covered in this post by Ciphergoth from a few years ago.