then why do states allow marriages where procreation cannot occur (and in some obscure cases require the couple to prove it cannot occur)?

” it would, in a sense, ‘get the state out of the bedroom’.”
How is the state currently “in the bedroom” wrt to marriage?

then why are you suggesting changing the name from “civil marriage” to “civil partnership”? that seems to imply that religion has “ownership” of the word marriage when it does not.

My understanding is that, here in England and Wales, and in Scotland, there’s no concept of ‘consummation’ in respect of a civil partnership. (Maybe it’s different in your jurisdiction.)

Re. Plyler v. Doe etc: in this case it would depend on how the law in questions. What difference does it make to a woman who has just lost her partner and needs to inherit that partner’s real estate in order to have a place to live, if the partner was male or female.
If the law on partnerships is framed to cover these kinds of practical matters which are of genuine ‘public moment’, we will not have a “Plyler v. Doe problem.”