It in no way diminishes the cis women who give birth"
You can say that, and I being cis-male can easily say 'Yup, I agree'.
But at the same time ... what if some cis-women don't?
What if their true feeling is that they don't like being referred to as a 'birthing person' or 'person with a uterus'? What if they are hurt or offended and don't like being defined by their reproductive abilities, and/or simply prefer terms like woman and mother?
I might logically surmise that some women will feel slighted, like trans folks are taking something special away from them, even though they are otherwise supportive. I imagine a scenario where an expecting person might visit a bookstore maternity/child-rearing section and find that every book there has a name like 'A Guide For Pregnant Persons', and every reference in that entire book uses terms like that, and 'birthing person', etc. There's going to be a lot of women hostile to a change of that sort.
I say things like this out of caring, I want y'all to succeed and get all the rights and acceptance that are due to you, it's just there's occasionally things that you're asking for right now that I just sense are going to make it more difficult for you, that I think might go over better a little later down the line. Asking the world, essentially, to stop saying 'mother' and use 'birthing person' from now on in all generalized cases (i.e. we don't know which term a person prefers) ... it's a big ask and risks a backlash is all I'm saying.
When I look back on how far gay rights have come in my lifetime, I get a strong sense that the support in general of cis straight women, played a big role in that process. Acceptance of gay rights always polled higher in their group than it ever did with cis straight males, and I'm sure still that's still the case. It's a factor that's at least worth considering IMHO