If "gender" is just another word for personality type it's a fairly harmless conceit, but when it leads to the opening of women's protected spaces to male-bodied individuals purely on their say-so that they "identify" as something other than male, women are in real danger.
Many autogynaephilic cross-dressers actually hate women for being what they want to be but can never be. Their motivation for entering women's protected spaces is not to blend in but to occupy and colonise, enjoying the discomfort of women perceiving a male-bodied individual in a women's space. Peeping toms, exhibitionists, voyeurs and other varieties of general creep are now "identifying" as women to gain access to women's locker-rooms and bathroom facilities - not to mention domestic violence shelters - whether or not they normally present as trans. Effeminate boys are being allowed to join the Girl Guides and go on residential camps, sharing sleeping and bathroom facilities with girls. It has been made explicit that the girls' parents are not to be told that their daughters are sleeping in the same room as a male-bodied boy, and any girl who expresses discomfort or objects is labelled a transphobe and publicly shamed.