The issue is differentiating between specific people, and when we are generalising.
If specific pregnant women find being called a woman upsetting and ask people to refer to them as men, that's not (much) of an issue. It's not causing confusion to other people and messing up statistics.
What we are discussing here is a research project specifically about women.
As has been said umpteen times upthread, not being clear about language risks statistical inaccuracy in the research, and difficulty in communicating the findings. Is that worth it to avoid upsetting a vanishingly small number of theoretical pregnant trans men who will likely not come into contact with the research anyway?
I, and many others here, don't believe it is.
(As an aside, I'd love to know what percentage of women identify as a man AND get pregnant AND still want to be referred to as a man AND want all references to woman, mother, etc removed from literature. It's got to be absolutely miniscule, yet keeping them happy is deemed by sme worth all the damage this is doing to women, non native English speakers, neurodiverse people, the visibility of women's health and countless other things. That's an interesting trade off which says a lot about how some people view women and mothers).
There are no gender equality laws. The Equality Act does not list gender as a protected characteristic.
The OP quite rightly doesn't want nonsense written in a document that will reflect on her.
There are reams of posts discussing how changing language in a non universally agreed way does affect society as a whole - maybe read some of them if you are interested?
Oh and if you believe my views are due to my 'low self esteem' rather than my critical thinking, it's not very kind to say I should essentially buck up and do better - why doesn't that equally apply to anyone upset by 'pregnant people'?
Your true colours are showing.