If women don't like having the "birthing parents" being appended - why?
It's the "and". It's the implication that "women" is not an inclusive term. It suggests "women" means something other than adult human females. And it's not clear what. Certainly you're not intending to include "transwomen", right?
You're mixing two sorts of language in a single clause. You're not describing two different groups, but you're framing it as if they are. It makes no more sense than "women and frauen".
And how do you keep it up? If you had to include the "and birthing people" the first time next to the first "woman", you have to include it every time, unless you're changing the meaning of "woman" mid-document.
Some sort of footnote, or bracketed clause the first time you use "woman" to indicate that this includes all female humans, regardless of gender identity, then lets the rest of the document flow. Define terms well, once, and the rest of the document is clearer.
If someone wants a document in Genderese (or German), then that's a separate translation. Putting "and birthing people" or "and frauen" next to every "woman" in the English version is daft.
Conversely, if the document is intended to be Genderese, then it wouldn't make sense to put "birthing people and women" everywhere either. Just "birthing people" is fine.