Why does The New Yorker use a diaeresis for some double vowels?

You can use a diacritic only when it’s necessary to prevent confusion, or you can use a diacritic consistently, whenever the pronunciation goes one way rather than the other. In the former case, you reduce the number of diacritics in the language. In the latter case, you reduce the amount of pronunciation ambiguity.

English has a spelling system insane enough to be quite comfortable with pronunciation ambiguity (the more English historical phonology I learn, the more annoyed I get about it). And diacritics have never taken off in English. So the move to avoid diaereses within English, in general, makes sense: Diaeresis (diacritic).

But that’s one language community’s decision. It’s also why Pinyin users aren’t too fussed about <ü>. German does not think the same way about <ü>; and many languages value lack of ambiguity over avoiding diacritics. They don’t want to have to think about how the word is pronounced; if you have to think, you might as well use ideograms.

That’s the general principles. In the 19th century, English was friendlier towards diacritics; hence the profusion of graves like learnèd and diaereses like naïve.

Why does the New Yorker persist in the 21st century, against the global trend in English orthography?

I give you: the New Yorker logo.

It’s a consciously old-fashioned affectation. Of the kind that the New Yorker hopes its readers will find cute.