It's important to know a bit about the venues in question. Mathematical Intelligencer isn't really a journal at all; it's literally a magazine, carried on the shelves it bookstores. It runs some original research but also poetry and jokes and general cultural coverage.
NYJM is, on the other hand, a serious (if online-only, lower-tier) theoretical mathematics journal.
Ted Hill's paper is light on mathematics. As Joel Fish, an assoc. math prof at UMass Boston described it, it's of the caliber of an undergraduate applied math homework problem. It's also packed with citations to psychology, ev-bio, and current events.
Arguably, Hill's paper was reasonable for Intelligencer. But it had no place whatsoever in NYJM, which basically never runs anything but hardcore proof-heavy theoretical mathematics. In the very most charitable interpretation, Hill's paper is an applied math exercise.
Here's where the plot thickens: apparently, Hill's paper didn't undergo normal peer review at either journal, and, in particular, was fast-tracked in (papers apparently appear in NYJM as they're submitted, not in annual editions) by an editor that vocally shares Hill's politics. In response, I understand that a significant number of NYJM's peer review board threatened to quit --- an understandable response, since Hill's paper is embarrassing in the context of the rest of what NYJM publishes.
I encourage people with strong opinions who haven't done so already to:
1. Read the current version of Hill's paper.
2. Skim the first version of Hill's paper, which had a coauthor and virtually none of the political content subsequent editions had.
3. Skim subsequent versions and notice how and where they introduced political content, and match that up to the dates Hill suggests the paper was submitted, first to M.I. and then to NYJM.
4. Select a few papers at random from NYJM and skim them quickly to get a sense of the venue Hill is angry he was rejected from.
I'm left with the impression that this was an elaborate troll, one NYJM didn't handle well --- but then, that would be difficult, since its editor in chief is out on leave owing to a grave medical problem.
Later
This has been flagged to the nether regions of the HN story rankings, and justifiably so! It's a political controversy! But it's frustrating that the story introducing Hill's side of this in Quillette was at the top of the front page and accumulated hundreds of comments, while an actually-informed story that critically analyzed the paper itself will get no attention at all. Consider that the next time you think about complaining about people flagging politics off the front page. The Quillette story deserved to be flagged.