> I've reviewed for high-status journals have said explicitly in instructions to reviewers (and I'm only weakly paraphrasing) "don't evaluate the methodological integrity or integrity of the conclusions, only evaluate how popular this is likely to be."

(Academic mathematician here)

I'm curious, how do they get away with this?

In mathematics, it's common and perfectly acceptable to turn down requests to review a paper. (You're not supposed to turn down all of them.) When I've done so, because I've already taken on too many reviewing assignments at one time, I've never gotten pushback from journal editors.

If some journal editor asked me to review a paper, and gave me instructions along the lines that you described, then I'd just tell them "I'm very sorry, but I'm unusually busy at the moment."