Gender: Noun
Sex: Verb
Indeed, what they have done is to change the definition of gender to fit their own, fluid world.
Wrong. Gender is a linguistic phenomenon for assigning class, in most languages masculine, feminine or neutral. Assignation can be apparently random but often corresponds to sex appropriate characterstics of the nouns classed. Individuals do not have gender apart from the gender assigned to the whole class of individuals. Women, being of the feminine gender in English no matter what they choose to call themselves. In French the noun “feminin” is masculine thus “le feminin.”
Sex is a noun in both senses: sex as in male or female, sex as in having intercourse.
Gender is a linguistic term, not a biological one.