Could we just stop all the debate by relabeling public changing rooms and showers to those with penis and those without?

No, we need to protect the meaning of "men" and "women". The fact that anyone can legally change their gender without transitioning is ludicrous.

Instead of that, society would be far better off to get rid of all the prudishness and phobias revolving around nudity, the body, and what-sex-sees-what-sex-naked.  If people just viewed the human body as perfectly natural and intrinsically beautiful instead of something shameful, embarrassing, offensive, etc., then people would stop giving a sh!t who sees them naked, or who they see naked, or who has what between their legs.  Naturists/nudists think nothing of it to see others naked or to be seen naked, and in general don't care in the least if someone is transgender.  It is one of the most irrational things in human psychology to be afraid of being seen naked, or offended by seeing the naked bodies of other members of one's own species, and it is even more irrational for someone's level of comfort or discomfort with being seen naked to depend on the physical sex of the viewer as if that made any actual difference.

I've been seen naked by people who have a penis, and I've been seen naked by people who have a vagina, and in neither case did it have any effect on me whatsoever.  Why should it make any difference to you?

The silly thing about this debate is,  its a storm in a tea cup. 

Trans make up .6% of the population.    I am a social outgoing person who only uses the restrooms when needed,  in other words not all that often.    I expect a trans person would be the same in that they would only go when its absolute necessary. 

Which explains why despite me being a very social person no one I know has ever described the scenario that this debate focuses on.   Yet lots have been the victim of bulling both in school and as adults and lots of women and a few men have experienced sexual assault plus lots have been physically assaulted and many have been robed spanning from childhood to old age.  

Yet none have reported the public change room/showers/toilets scenario as this question suggest is common.   In stead its a non event.  

No.  What we need is separate cubicles by the public area with curtains and built-in showers.  They used to have those at a swimming pool I used to go to and they work perfectly.

"other people wouldn't have to see body parts they shouldn't have to see in semi-public naked places."

Ok but I don't think anybody wants to see anybodies genitals regardless if they are the same as their own or not. If you (general you not personal you) don't want to see someones genitals in a changing room then don't look but this is probably a moot point since I don't think any pre op trans people will get naked in front of anyone anyway. 

The best fix I can see if to have rooms for men, women and a gender neutral room. In all rooms there should be separate stalls (don't most have these anyway?) that people can shower and change in. This way everyone, not just trans people, can have privacy if they are not comfortable changing/showering in front of people and the gender neutral rooms are nice not only for trans people but for families and people with a care giver that is a different gender.