I don't think words need to be gender neutral. Grammatical and biological gender are not really the same. I think this urge to clean languages is a bit detached.
Personally, I have no skin in the game of gendered language. Sometimes I think it's exaggerated, sometimes I think it's necessary. I do have a hard time changing how I speak, old habits die hard. As far as people and everyday communication is concerned, I address people the way they want to be addressed. Nothing to do with gender, just general politeness. E.g. I wouldn't use a nick name people hate, so why would I insist in calling someone "her" (or "he") if they don't want to?
I wasn't referring to calling someone another gender. Doing so is just minimum courtesy. I do believe that courtesy cannot be mandated though and I would not want anyone having it mandated for my sake.
I meant words like mailman and such. Of course a mailman could also be a woman. I think calling someone a mailwoman is fine, but the word does not carry intrinsic offense.
We don't disagree, I think. Gender neutral job titles are ok, as far as I'm concerned. Mostly that is, as the female jobs are, historically, more often lower income jobs in the same domain (nurse vs. doctor comes to mind). Coming back to courtesy, if a female mailman prefers to be addressed as mailwoman I would do so.
Funny side note, the German language has some interesting edge cases. E.g. the rank of Hauptmann (Captain in the army and air force) usually isn't gendered, the other ranks aren't neither. So usually female soldiers of that rank are addressed as Frau Hauptmann. The funny thing is Hauptmann is also last name... The plural of the rank Hauptmann is gender neutral again, it's Hauptleute...