I would go down the line of what doesn't need to be sexed due to not necessary or common sense.
Such instances I can think of are:
Parents and carers instead of mums and dads is inclusive of children being raised by grandparents, adopted, etc.
We are looking for volunteers to help with the cake sale (instead of mums and dads)
Such instances don't lose much from being inclusive however, some instances meaning is lost could be:
We are looking for mum's and dads to help drive kids to x (if changed to people could end up with safeguarding risks, as mum's and dads are informally seen as less of a safeguarding risk than ransoms)
Our local book group for mum's (nothing wrong with either sex joining, but if it's already heavy with one sex could make males joining uncomfortable)
Our maternity yoga group for mother's to be(I feel this explains itself but some people think father's to be can give birth, I'd be adding a caveat like 'pregnant people' as well as MTB not instead of, arguing that the word mother is very emotional and part of the language that eases pregnant women in to motherhood.)
Without knowing your organisation it's hard to come up with specifics, but the main reason for keeping sexed words are:
Clarity- whether medical or just to signpost who you are talking to in shorthand. Long-winded explanations lose interest.
Respect- most people prefer men or women than menstruaters and wankers.
Universal understanding- if you use roundabout terms like people who lactate you're going to end up alienating people who don't understand the words through language or education barriers.
A good idea would be to perhaps test drive them in a meeting. See how people really respond to, " Can all the menstruaters line up here and all the prostrate Havers over there?" Then watch ensuing indignation and chaos.