My doctorate is irrelevant to the truth

It sure is. I've seen a PhD who didn't read the only textbook he had referenced in his thesis, which proved his idea that teachers were doing it wrong and he wasn't, was wrong. 😂 Should've listened to the people who teach it (or actually read the textbook he referenced 🙄 ).

which makes students of math feel inordinately inferior

They don't. All students get this correct. It's only adults who have forgotten the rules that get it wrong.

these gotcha-style math memes IMO deepen students’ belief that they’re just bad at math

Nope. Students never get these wrong.

proofs mean something very specific to me and I can’t yet imagine what that looks like WRT order of operations

All you have to do is see which way gives wrong answers for 2+3x4 and you've proven which ways don't work 😂

note that conventions aren’t necessarily “optional”

Yes they are.

when being understood is essential

You don't understand how to do 2+3x4-5 without knowing which conventions people use for the order of the plus and minus?

Here I am only concerned about the next generation of maths student and how viral content like this can discourage them unnecessarily

It doesn't. None of them get it wrong. 🙄