I think it's more of an all or nothing thing. What you're saying can be viewed as selective discrimination. A similar scenario I envision would be a group of biological females who decide to form a club of some sort perhaps in addition to being female, also share a common experience of childbirth. Transgender proponents and supporters would most likely cry foul if such a group didn't want a biological male identifying as a woman in the group.
I'm actually surprised that there has not been more of a public assertion by biological females who have given birth as to uniqueness of such an experience which, like it or not, absolutely excludes biological males in any form from identifying with said experience. I recall when my wife, who with one of our children was in labor for 35 hours read that the musician Sheryl Crow who adopted or had a surrogate give birth said something to the effect of: "When we gave birth to.....". My wife's reaction was pretty visceral: "Um, YOU didn't give birth to anyone there, Sheryl!". I'm sure an argument could be raised that there are many biological females who don't give birth and no less a woman for not doing so. I guess my point is childbirth is real and unique and can't be identified with unless you're a biological woman who has given birth....
I recall reading some things after that woman's march in the U.S. that some biological women were not accepting of transgender males identifying as women joining the march for the cause of women.