Figured I'd add these comments.
"A trans man with a cervix needs cervical screen. This has to be communicated or people die"
I don't believe this narrative that as soon as they start identifying as male or a special gender, pooners become incapable of guessing that an invitation from the gynecologist telling women over the age of 25 to get a cervical cancer screening would concern them as well. Granted, some (many) troons are dumb as bricks, so the risk probably isn't zero, but for the most TiFs are just going to pout because the invitation didn't affirm their gender feels and then go to the gynecologist anyway.
On the other hand, expressions like "vagina-havers" and "people with a cervix" are going to be inclusive of pooners, but it excludes/alienates a much larger group of women.
To begin with, it's going to cause confusion for some normie women who aren't up to date with the latest troon lingo. It's probably possible to guess the meaning of some of these expressions without prior exposure to gender woo woo, but others like AFAB are more vague.
Then there's a large group of women who do understand the meaning of such expressions, but object to being referred to as "birthing bodies" or "uterus havers". If you're aiming to be "inclusive" then insulting a large part of your target audience/group isn't a great way to go about it.
On top of it all, in a large number of Western countries, there's a growing number of immigrant women (immigrants in general, but the women are more relevant to this subject) who have a poor grasp of the main language of the country they live in. These women are far more likely to understand the meaning of the word "woman" than "bodies that breed" or "cervix havers". In fact, in a lot of cases they haven't received any proper education about female biology and/or sex education, so they might not even know that they have a cervix or a uterus. (Ironically TRAs are typically supportive of lax immigration/multiculturalism policies and often think it's literal nazism to expect immigrants to adapt or learn the local language, yet when it comes to abstract troon lingo foreigners are just assumed/expected to automatically understand it)
If a medical professional has the choice between a) using confusing "inclusive" language created to affirm the feelings of a small group of narcissists and b) actually understandable and inclusive language created to reach as many people as possible in a certain group then that person should always go with b), and b) involves the use of the words "woman" and "female" – not "birthing bodies" or any other ridiculous euphemism troons have come up with