Is that really analogous? English doesn't typically gender its nouns, so distinctions like "water/waitress" are deliberate, if not always conscious, attempts to draw a distinction on a basis of gender. It carries a baggage of expectations because the construct itself expresses those expectations, would not serve any semantic purpose if it didn't. I would tend to assume that there's less baggage attached to a basically grammatical construction like "Latino/Latina".
The value of going out of your way to write "Latino/a" or even defaulting to "Latina" seems to be in the action in itself, in making the point that the male is not a natural default, rather than a correction of a shortcoming in the language. If we were just looking for the most efficient route to parity, we'd simply delete the female gender altogether. (And doesn't that make me sound like some kind of linguistic incel.)
Generally speaking, more than a movement away from explicitly gendered Language monikers (though there are some holdovers that are being phased out currently, e.g. Englishman, Frenchman, Dutchman, etc.), the move is more part of a larger movement away from substantivizing descriptive adjectives. So rather than "he is a readhead/Jew/black/etc.", you keep the terms as adjectives: "he is redheaded", "he is black", "he is Jewish", or to hyphenate the adjective with an agent noun: "He is a French-speaker". I think this has to do with an increasing uncomfortability, at least on this side of the Atlantic, with the implication that the speaker is thereby reducing a whole individual to one singular characteristic or attribute.
One interesting thing that would undercut this observation
vis-à-vis demonyms would be that there are some language/nationalities for which you absolutely can substantivize, e.g. Italian, German, American, Mexican, Argentinan, Brazilian, African, which would seem to suggest that it's more about phonotactics/declinability than it has to do with the trend I noted above - "an English" just doesn't sound right because it doesn't end in a way that allows us to either identify it as a demonym, or else decline the word into one. However, at least in America, you can definitely see the effects the above-noted uncomfortability has on
certain of the demonyms, as even though they exist, you either see American English-speakers actively avoid using the terms, or else immediately furtively glance around upon using them to make sure nobody heard them/nobody heard them who would be offended by their use. The certain ones I have in mind specifically are "Jew" and "Mexican". I would say with "Jew" you feel this most viscerally; it's a term you will actively notice English-speakers tying themselves in knots trying to avoid saying. To the extent that you don't even really see it expressed in the plural anymore (unlike "black", which is, itself, invariably "blacks" if used this way, and never "the blacks"), it's almost invariably "Jewish people" rather than "Jews", to say nothing of "the Jews". "Mexican" gets this to a far lesser degree - usually the word gets dropped and then the speaker looks around awkwardly, unsure exactly "if we're allowed to say that anymore". Black (as in: "he is a black" or "look at that black") has been phased out so completely of American English that its use is followed not by furtive glances, but a full on bracing for a punch to the face.
Might be a regional thing in America, then, because when I lived there I often heard the expression "Latin guy", including in reference to my Latin self.
Historically, Latin was also often used to refer to peoples. Indeed, the ancient inhabitants of Latium were the Latins, and their language is Latin. Later, western Europeans were collectively known as latins to Greeks and Arabs, and sometimes northern Europeans would refer to romance speaking southern Europeans as latins. It looks like a totally fine term to differentiate people with roots in Latin America to those with roots in Anglo Saxon America.
That's certainly not how I've experienced them used, no. Latin = Latin language and nothing else in my experience (speakers of Latin = Latin-speakers or Latinists for later scholars/enthusiasts of the language; people from Latium are Latians or "inhabitants of Latium" or some variant of that).
I have heard "Latin guy", but two things:
1) Note that you aren't using the term substantively, but rather adjectivally, which is mostly what I was talking about. Even in the context of "Latin guy", I don't think you would hear it as "The Latin" or "The Latins".
2) I've only heard it in the context of like, movies from the 40s and 50s. As I noted in the post you quoted: if I heard someone use that today, I would think "old guy racist" in the same way as someone who uses "negro" or "chinaman" or something like that.