This reminds me of the signs in the local fertility clinic in my nearest NHS hospital. In an effort to embrace diversity and be non-discriminatory, which is laudable, the signs depict various cartoonish characters as either singletons or in pairs. The only problem is that when you count them up, there are seven adult male characters and only four adult females. It always amuses me to see them as it is as though females are somehow the minor factor in the process of assisted conception. 
Obviously, no one that works there has noticed this, but it has always struck me as an illustration of what can accidentally happen when people get too wrapped up in current socio-political modes. You can end up alienating or minimising the very people your service or actions are attempting to treat, and that can erode trust.
This BMA document is a disaster, not necessarily because it attempts to force a language change onto the medical establishment that would confuse many service users, but because it says to pregnant women: "you are not a expectant mother anymore in our eyes, you are a pregnant person." And that is quite a big shift. It takes away all the biological, social and cultural associations that are encapsulated by the meaning of the word "mother" from the pregnant woman. To me, it acts to sever the biological process of conception, pregnancy and birth from the social, cultural and political implications of that biological process.
The ideological side of me thinks that it is quite interesting, to be honest, but in reality, it is utterly unworkable.
Again, I find it amusing that the BMA document is about "effective communication" when the suggestions given will probably cause more ineffective communication than at present. You have to consider that many midwives and obstetricians deal with pregnant women that do not have very good English language skills; in such cases, it is a very good idea to stick with generally understood and known terms. Mother is a concept in every language; the notion of a "pregnant person" is not.