I agree celestina - the discussion on this thread has been at least more measured, and my terse and emotive earlier contributions came from the frustration I felt about the plethora of other threads on the topic.
I do see the point about women being "required to shed decades of very strong socialisation," regarding some women only spaces like toilets and showers. However, as I think someone else mentioned, such demarcations by sex aren't the "norm" in all countries and cultures. In 1984, I encountered my first unisex loos, showers and dorms in Norway. Yes, it felt strange to me but not for Norwegians. One could argue that white British people have been "required to shed decades of very strong socialisation," to enable Black, Asian and minority ethnic people have the same rights to employment, education, housing, representation, etc. as they do. So, I feel quite queasy about applying that argument in this context, iyswim.
I agree that girls and young women will have shared many of the same experiences of growing up female, including the barriers and prejudice they faced. Of course there will be variations in those experiences - wealthy privileged girls will probably have vastly different experiences than poor ones, white girls different from Black girls, etc. There may be some contexts where one might identify as much or more with the experience of someone of the opposite sex, for example where both had the same disability, both had divorced parents, both lived in a rural area, etc. Identity, how we related to others and our experiences can be quite individual.
There also seems to be the assumption in your post (correct me if I've got that wrong though!) that because trans girls won't have the shared experience of being a girl, they will by default have had the "normal" experience of being a boy, and never have experienced any of the discrimination, abuse or disadvantage suffered by girls within a patriarchal society. I don't think we can assume that at all. Trans children can be subject to horrendous bullying and abuse for failing to conform to the gender binary - abuse from boys, from girls and from adults. Because they will probably be seen as "feminised," (as gay boys may also be), my hunch is although their experience won't be identical, they'll have more in common in terms of taunting, sexual bullying, exclusion and assaults with how girls experience growing up than how boys do.