They are completely correct. The gender of a word depends upon the language, and sometimes the usage.
The “gender is a grammar construct” is a fake argument introduced in the 90’s by the new “gender studies” academics. A word being masculine or feminine has nothing remotely to do with a person being male or female. A female can have masculine traits and a man can be feminine, but that has no effect on their gender. Look up Gender in a dictionary from the 80’s and you will find no references to such rubbish. Regardless of subject (pipe fittings, nut’s and bolts, electrical plugs or biology), you will find 3 options; Male, Female and None/Neutral. They want to change the language to the point there are no words to convey your argument. Maybe next, your official govt id will have to define you as cisgender or trans, since male or female are no longer legitimate genders?