Jesus, I can't imagine being on duty in the ER when Fred Sanford rolls in with a heart attack.

The correct answer is to show some respect & call people what they wish to be called - it's super simple. There are however norms to look at particularly in professional writing and academia that usually try to set acceptable norms & standards by this principle. This whole conversation was more akin to a pointless thought experiment than anything.

Honestly I decided to research this because I'm a bit bored and it seems that in professional writing it's a mixed bag on what the appropriate gender-neutral term is and if we need one at all. Some of this is because of the vast diversity of the English speaking world. From it's humble isle in Europe, to north America, to Asia, to Africa, to it's cozy corner of the southern hemisphere cultures of each are going to dictate how each cohort discusses gender-neutral terms. But the focus of the discussion seems to be primarily on the gender binary of man & woman and exclusionary of nonbinary/gender fluid/trans people. Here are a few pieces that I've found discussing the issue:

Lateral Magazine: Keeping it neutral

Hakai Magazine: “Fishers” or “Fishermen”—Which Is Right?

Ghoti Papers: Should we call them fishers or fishermen? (abstract)

The Sun: Female fisherman blasts BBC for using gender neutral term ‘fisherpeople’ (I only included this one for shits and gigs due to its sensationalized nature & I genuinely found it comical)

ABC (Australia Broadcast Company): Is 'fishermen' a sexist and exclusionary term?

The University of Auckland: Fishers or fishermen

Angler is a good alternative too. I mean if they prefer fisherthem, whatever, it's just such a clunky word lOl

I was thinking fisherperson, just because it feels less clunky than fisherthem but what the heck ever - if they want to be a fisherthem, have at it haus do you lOl

Sounds like a beer barn