I agree with your concern OP. The issue is that the NHS appear to still be conflating sex with gender which various institutions have now stated the bleedin' obvious confirmed that is not helpful in a medical setting.
As we know, sex is immutable and determines many aspects of medical treatment. Any disconnect with biological reality in medicine introduces risk and potential danger to all patients.
Thankfully we are now seeing clear water between sex and gender - our helpful poster asugar has confirmed it themselves so there seems to be consensus on both sides of the debate.
We all know that 'gender' or 'gender identity' is not medically significant so we should not be removing a sex based term 'mother' 'pregnant woman' etc on the grounds that some people have a specific 'gender identity'.
Gender identity is not relevant to a person's sex and should not be allowed to cloud medical communication. The difficulty with using the term 'people' is that is creates confusion by including a group (males) to whom the message is not relevant.
I was going to suggest that they could use pregnant women and transmen/non binary but it occurs to me that there are many other gender identities other than these two. There appears to be no consensus on a 'master list' of gender identities so this runs the risk of being wrong or missing a gender identity.
It also doesn't address the issue that many gender identities seem to be non-sex specific so a person of either sex can claim a particular gender identity for example cloudgender. Then there is the problem of gender identities like pangender - which means that someone has more than four genders. Or multigender which is also more than one gender (although to avoid overlap with pangender, maybe less than 4? - who knows).
So that then leads me to wonder how the NHS can take gender into account at all in a sensible way. If they are trying to be fully inclusive, they can't realisitically list people with the gender identity of transman, but exclude other genders like pangender for example, but then pangender could be of either male or female sex.
In conclusion, I think we need to follow the science and say that as sex is the only key element for medicine, and confusion around that will introduce unacceptable risk for all, we need to retain our sex based terms.
Transmen know they are of the female sex. Acknowledging their sex is imperative for appropriate and safe medical treatment. Their gender identity is not relevant in medical situations so for their safety and for the safety of everyone else we need to stick to absolute clarity on male and female.
Obviously on a 1-1 basis, transpeople can request to be addressed in the manner that makes them feel comfortable but we need to maintain the appropriate words for the majority of the population.
www.safeguardinginschools.co.uk/wp-content/uploads/2019/09/List-of-Gender-Identities-1.pdf