You’re mistaken about the lack of “hard lines” distinguishing the sexes, though. The difference between male and female is unambiguous in biology. “Trans women” are, by definition, not women.
That is emphatically false. There are innumerable biological differences between men as a whole and women as a whole, and while these different factors largely correlate, they do not necessarily fit neatly into one box or the other. Is an XXY individual with a penis but undescended testes and low levels of blood testosterone and few androgen receptors "biologically" male or female? What about an XX individual with ambiguous external genitalia, high circulating testosterone, and a high number of androgen receptors? What do you make of the fact that females with congenital adrenal hyperplasia are far more likely to identify as LGBT? You are oversimplifying the biology.
That said, the right to create an exclusive space is a fundamental constitutional right. En plus, for socially marginalized groups, it is a societal benefit for them to have a space exclusive to them. I support the creators of this social media app.
It's appropriate to discuss generalities. It's appropriate to discuss individual cases. What is inappropriate is dismissing individual cases to come to a general conclusion, and then insist that it applies universally.
This is also in the context of trans people the vast majority are not biological outliers simply people identifying as something different to their unambiguous biological sex.
To make this claim, you would have had to find an exhaustive list of biological sex differences, and check a large representative random sample of transgender individuals to see whether all of those biological sex traits aligned "unambiguous[ly]" with their assigned birth sex.
Since I am quite confident that this work has not been done, may I suggest deferring to individual people to tell you what is going on in their bodies? While imperfect, self-reporting is still epistemologically far superior to you just pulling this claim out of your ass.
Women can be sexed at birth as female, male, intersex, neither; women can have genes for XX, XY, XXY, etc; women can have zero or more genitalia; women can have masculine, feminine, androgynous, mixed facial bone structures.
Each of these is a valid subgroup of women which can, if necessary, be described as a subgroup. Normally, just “women” should suffice, but the app linked by this post actively excludes at least one of those subgroups from the label “women”. So it becomes necessary to discuss those subgroups by name, such as “trans women” and “black women”, in order for discourse to occur.
They might be “male at birth” or “intersex at birth” on certain medical paperwork, and those physical sex characteristic will remain unchanged in subgroup “at birth” regardless of any shift in gender or medical alterations to their present-day sex characteristics.
(To avoid any possible confusion, I’m keeping in mind that “male” is sex and “man” is gender, as this is often confused in discussion of these topics. One’s sex is a physical characteristic like one’s eye color or skin tone; most people assume that everyone has just one and that it doesn’t change, neither of which are true. One’s gender is a behavioral characteristic like accent or musical tastes; it can’t be reliably guessed from any physical characteristic, and it can change at any time, either gradually over years or all at once at a coffee shop or anywhere in between.)