That is, after all, Wikipedia and I think they have it wrong. Those are examples of natural gender, not grammatical gender.
I think the clearest way to explain what’s going on is to give a history of the word “nurse”. There was a Latin word “nutricia” which meant a woman who nourishes.
This became an Old French word and then a Middle English word. It meant (as a verb) to breastfeed or (as a noun) the person who did the breastfeeding. Then it became a word for a woman who takes care of young children. Then it was used for a woman who takes care of people at hospitals. During all this history, it was assumed that only women would have this job. Then men began becoming nurses. People began referring to them as male nurses since they thought that otherwise people would assume they were women. Now people use the word to mean a nurse of any sex.
But the word is “nurse”. So the comment is most relevant.
And yet, in languages of Latin origin certain words may have both masculine and feminine versions. For example, in Romanian the word **student **(= university student) indicates a male student whereas the word **studenta **indicates a female student. Similarly, the word **elev **(= pupil, student) indicates a male pupil whereas the word **eleva **indicates a female pupil.
Romanian call nurses (doctor’s) assistants, with the word **asistent **indicating the male nurse and **asistenta **indicating the female nurse.
Nonsense.
https://www.o-wm.com/article/my-scope-practice-retrospective-civil-war-nurse
https://ahec.armywarcollege.edu/exhibits/CivilWarImagery/Civil_War_Nurses.cfm
http://broughttolife.sciencemuseum.org.uk/broughttolife/techniques/nursing
FWIW, I certainly don’t think that nurse implies female. French (at least Quebec French) is similar to what Nava said about Spanish. The words are infirmier and infirmiere.
Now here is a curiosity. Everyone agrees that an actress is female, but more and more I see actor used for either males or females (and anyone in between). Waiter is another example.
Australian here. I know a nurse very well, and if he is asked what he does for a living he just says, “I’m a nurse.”
I would never use the expression, “male nurse.” Nothing to do with being PC or anything like that, it just sounds weird to me.
Also a woman can be a “hero” but a man is not a “heroine”.
This goes hand-in-hand with the trend toward gender-neutral terms for jobs (e.g. police officer for policeman, flight attendant for stewardess) as most jobs become less exclusive to one sex or the other. I expect we will continue to see the feminine form for other job descriptions gradually decline in use over time.
Yes, and it’s all a matter of familiarity…
For me, as someone who is 49 years old, it still sounds odd and grates a bit to read/hear a woman referred to as an “actor” instead of an “actress”; but a word like “aviatrix” for a “female airplane pilot” feels very old-fashioned and archaic (usually a word today used for laughs to imply a 1920s-era style of sexism).
It’d be nice if role or title terms created by appending “-man” to them were automatically gender-neutral (like with “mankind”), but invariably they were used for roles/jobs “traditionally” done by men, so I can see how women in these roles feel like they need to push for a neutral term to be the norm so people aren’t constantly surprised, with an “oh! you’re a woman!” reaction that is almost always negative.
The term “Chairman” has, in my experience, successfully become “Chairperson” or more amusingly, simply “The Chair”. (Which use always makes me think of the awful song lyric from Neil Diamond’s “I Am, I Said”, where he regretfully notes that nobody heard his depressed mumbling, “not even the chair”).
“Policeman” => “Police Officer”, OK, that has some traction… But what about “Fireman”? (Serious question, I don’t know the gender-neutral term for this - maybe because I have literally never seen a woman fire-person, while I have seen plenty of women as police officers.)
And hey, what’s a man called who gives out parking tickets? A “male meter maid”? LOL
Oh, another one is the gender and relationship neutral term “partner” for wife, husband, or spouse, but one step up from “Significant Other”, I assume, in the level of commitment.
One used to simply refer to one’s “boyfriend” or “girlfriend”, or “husband” or “wife”, which I guess made people in same-gender relationships uncomfortable in revealing that detail (especially prior to SSMs being legal), giving rise to the term “partner”… Which in turn initially essentially implied a monogamous same-sex relationship (why else wouldn’t you just say “boy/girlfriend” or “husband/wife”?) until maybe the last 10 years or so, when I’ve started to see the term used generally and generically.
I personally never refer to my wife as my “partner”, which I guess makes me part of the problem they’re trying to fight against, but I’m sorry, it just feels really weird and wrong to do so. Maybe because I have long referred to people I play bridge or racquetball with as my “partners”, neither of which I do or have ever done with my girlfriends/wife. The term never had a romantic or life-permanent or long-term overtone to me, and I don’t really want it to do so.
Firefighter
Bylaw officer
You seriously haven’t heard of firefighters? It’s been the defacto term for decades.
Meter butler?
Ah, of course I have. It just didn’t come to my mind as a term for a woman in firefighting gear… Which is obviously the problem here. 
And… “Bylaw Officer”? Are you joking? I have never heard that term and would have no idea what it meant if I’d seen/heard it used out of the blue (here, I only know it because you told me it was the neutral term for a parking meter enforcer)
Actually, the colloquial term in NYC for the latter is “Brownie”, because of the brown uniforms they wear to distinguish themselves from police or traffic officers (the uniforms otherwise look very similar).
As for languages other than English, the Swedish term for a Registered Nurse is sjuksköterska, regardless of sex; although the word historically is grammatically female gender. Except for in Finland Swedish, where it’s called sjukskötare (the corresponding male gender form).
Wikipedia had it right all along, until January 22, 2020, when some nincompoop blundered in and changed “natural” to grammatical." Expect that to be reverted too.
I think “meter maid” became popular because of the alliteration. More seriously, Parking Enforcement Officer (or Parking Control Officer), although a mouthful, seems to be common as the official term.
“Baxter” (but not aviatrix or actress) has been deleted from the Oxford Dictionary of English, so someone must know some of those words are not being used much.
Roles/jobs like “woman”, you mean? 
“Man” was AFAIK more gender-neutral (if grammatically male) in old-school English, but, sure, terms like woman (= wifmann) were grammatically male. “Wif” wasn’t feminine either; it was neuter.
I wouldn’t pay too much heed to the grammatical gender of these words, which in English has not been a thing for centuries.
Traffic warden?
A bit of a side thread, but there’s a parallell in Swedish. The common term lapplisa probably became popular because of alliteration. As *Lisa *is a female name, it seemed appropriate at a time when most parkeringsvakter in Sweden were female (to the best of my knowledge, they might still be!)
The obvious male counterpart would be a lapplasse. For some reason though, that never really has caught on!