I might be wrong, but this sounds a lot like someone trying to speak for the trans community, rather than letting them speak for themselves.
If you have just given birth, you are biologically the mother. Your social gender identity is separate. Also, the number of people caught up in this situation is tiny. Most of them will also be accepting of the need for medical clarity, over preferred language, so long as they are addressed appropriately outside that.
99% of the time, what is between your legs has no relevance to day to day interactions. Maternity care is an obvious exception, and should be treated as such.
If someone from the trans/non-binary communities wants to educate me on this, it would be welcomed, but from what I've heard, this is not generally even on their radar, let alone a big issue.