It's an interesting one this.
I think maybe parent 1 / parent 2 etc may be the way forward and with a second part as others have posted for information for the child only.
I agree that mothers / fathers don't need to be the bio parent in order to fulfil that role, so really all that is left is either the stereotypical roles of mother / father, and/or the sex of the parent.
So eg my DH is a bloke but he's more stereotypically maternal than me. That doesn't mean that I'm the father and he's the mother and society would think us odd if we had got our children to describe us that way.
So it's down to sex, then. Men are fathers and women are mothers and they fulfil the role however because obviously gender roles = bad...?
My gut feel is that both men are fathers and I feel uncomfortable with a man being legally the mother. But I'm not sure why. All the laws and so forth deal directly with pregnancy / giving birth and so forth so no issue there I imagine.
I suppose maybe it just feels like a lot of "female" roles are being occupied my men at the moment? And with things the way they are the women who used to do them get pushed out. Like there was some big ceremony we were watching last year and there was a song about how everyone could be free and do whatever they felt and wasn't it great and this was accompanied by young women in skimpy clothes + men in pretty frocks / skimpy clothes. And I thought, well they haven't got a contingent of women in there expressing their liberation by not adhering to the beauty standard. Or, being over 40 or something.
Dunno. It's not an entire thought but it's just in a society which thinks men are better, then to have them colonising the only areas we were deemed to be any good for feels like a bit of a loss. And maybe a bit of a worry. So it's like, well if women won't play ball (adhering to ornamental status, being satisfied in a traditional mummy role) then we can ditch them and just get men to do it instead.