For example, in German 'Der, die, das' are designated as masculine, feminine and neuter - but 'the girl' is 'das Mädchen' I think?
All words ending in -chen in German are neuter (i.e., take the article "das" in the subjective form). More generally, in most languages that have genders, it's the word, not the thing described, that has a gender. The most common vulgar word for a penis in French is "la bite" (French people on holiday in the UK love taking pictures of places called the "Big Bite Snack Bar") and the standard word for a vagina is "le vagin". A person is "la personne" but people are "les gens", masculine. A car is either "un auto" or "une voiture".
Incidentally, the Germans have made their own attempts to eliminate what they see as gender-oppressive language. Consider, for example, the word "Arbeiter" (worker, labourer). It is inherently gendered in a way that doesn't arise in the general case in English, and so there has also always been "Arbeiterin" for a women worker. (Like actor and actress in English, but you can add "-in" to pretty much any job title, including new ones that have just been invented, just as you can make them plural.)
Now, to be inclusive, if you are describing a hypothetical worker, you should say "Arbeiter oder Arbeiterin", but that's a bit long. So a few years back, someone came up with the idea of "ArbeiterIn", where the capital I hints that you should go back to the start of the word (because all nouns in German start with a capital letter), very much like "D.C. al Coda" in musical notation. So it fits "Arbeiter" and "ArbeiterIn" into one word.
But then someone pointed out that this format excludes non-binary (etc etc) people. So a star gets added for them: "ArbeiterIn". If you take this to its logical conclusion, to refer to members of Islamic State you should use "IS-MitgliederInnen", which nicely avoids oppressing all of the genderqueer suicide bombers out there (whom IS of course embraces with open arms, to save them from the kind of awful persecution meted out to the OP's line manager).