It's just a shame you can't acknowledge their gender identity. It's ridiculous to say sex isn't real (as some do) but equally ridiculous to say that gender isn't real.
Their "gender identity" is "acknowledge[d]". The problem you are having is that we are querying why it logically follows that, for example:
• acknowledging that someone male experiences gender dysphoria and that they want to be known as Karen means that we should place Karen in a women's prison,
•that acknowledging that someone male has gender dysphoria and now wants to be called Laurel means they should take one of the New Zealand places for the Olympics,
•that acknowledging someone female has gender dysphoria means they should be able to strip search an incarcerated man who objects to being seen naked by a female person who is not his wife.
extract
The plaintiff [Rufus West] alleges that in 1995 he embraced Islam. He states that Islamic law prohibits him from exposing his nakedness to anyone except his wife. The plaintiff also states that under Islamic law, "males and females are identified and determined by the sex that Allah (i.e., the Creator) created them with at birth." …
The plaintiff says that on July 2, 2016, after a visit with a friend, he went to the strip search area to be strip searched under a policy that requires all prisoners to submit to a strip-search after a contact visit. Several officers were conducting strip searches.
According to the plaintiff, when it was his turn to be strip searched, defendant Buhle, a female correctional officer, approached him and ordered him to strip. The plaintiff states that he asked defendant Buhle how she was able to do that and she responded, "I'm a dude." The plaintiff says he looked at the other correctional officers, "to see if this was a prank," but that they avoided eye contact with him. He alleges that at this point, he "started to panic because he knew that Officer Buhle was a female based on her female features (breasts, face, voice and demeanor) and that exposing his nakedness to her would be in violation of his Islamic beliefs ….
The plaintiff indicates that "[i]t was later brought to [his] attention that Officer Buhle is a female claiming to be a male and therefore is afforded all of the duties that the male officers perform without discrimination."
The plaintiff alleges that in anticipation of another encounter with defendant Buhle, he wrote defendants [GBCI Security Director John Kind and GBCI Warden Scott Eckstein] and requested an "[e]xemption from exposing my nakedness to the opposite sex … because it is against Islam." On July 12, 2016, defendant Eckstein allegedly denied the plaintiff's request: "I have reviewed your correspondence and have also discussed your concerns with our Security Director. I have reviewed the situation and the officer in question is a male and is qualified to complete these duties. If in the future you are directed to submit to a strip search by this individual or any other male staff member it is my expectation that you will comply."
From reason.com/volokh/2018/08/15/muslim-male-inmate-objects-to-strip-sear/