LGBTQIA+ college acceptance in Gender Specific colleges

If you do not conform to the traditional gender binary, can you still attend a gender specific college?
For example, if you were biologically born as a male but identify as a female, could you attend a women’s college. Essentially I’m asking if transgender people can attend gender specific colleges. This includes all transgender people, whether they have received gender reassignment surgery or not, whether they appear cisgender or not, and whether they are closeted or open.
Also, if you did not fit into the standard “male” or “female” gender roles and deviated, could you still attend a gender specific college? For example, if your gender expression was fluid, or if you were bigender/trigender, could you still attend a women’s college if you identified most strongly with being a woman?
Regardless of biological sex assigned at birth and gender identity, could a person attend a gender specific college? If not, isn’t that rather exclusive? Why do gender specific colleges exist? What purpose to they have?

(ALSO: I do not mean to offend anyone with this post. I am not being sarcastic by any means. I have recently learned about gender identity and how it is a social construct and I want to know more about this topic from different viewpoints.)

Your answer will depend on the school. Wellesley, for example, will consider any applicant who lives as a woman, including candidates assigned male at birth. See #6 and #7 under FAQs:
http://www.wellesley.edu/admission/faq

Mount Holyoke accepts transgender women. Here’s a paragraph on their rationale

“1. Is Mount Holyoke College still a women’s college?
Yes, Mount Holyoke remains committed to its historic mission as a women’s college. Yet, we recognize that what it means to be a woman is not static. Traditional binaries around who counts as a man or woman are being challenged by those whose gender identity does not conform to their biology. Those bringing forth these challenges recognize that such categorization is not independent of political and social ideologies. Just as early feminists argued that the reduction of women to their biological functions was a foundation for women’s oppression, we must acknowledge that gender identity is not reducible to the body. Instead, we must look at identity in terms of the external context in which the individual is situated. It is this positionality that biological and transwomen share, and it is this positionality that is relevant when women’s colleges open their gates for those aspiring to live, learn, and thrive within a community of women.”
https://www.mtholyoke.edu/policies/admission-transgender-students

Smith does as well

I think most of the Seven Sisters came out with trans inclusion policies this year.

Here’s Bryn Mawr’s:
http://www.brynmawr.edu/pensby/GenderIdentityandExpression.htm

Yes, the seven sister schools will all consider transwomen for admission. Wellesley is perhaps the most strict - you must have had a “consistent identity as a woman” to apply. Mount Holyoke, on the other hand, is the least strict - they welcome applications from anyone who is not cis male, e.g. someone born male who considers themself to be gender fluid or genderqueer is still eligible for admission. Smith and Bryn Mawr are between the two; you have to check the “female” box.

That said, I can’t imagine why a person born male would want to attend a single-sex women’s college. The purpose of a women’s college is to allow women to experience an academic environment where their abilities are not questioned and their voices are not silenced because they were born female. I see no advantage to a person who was born male, and I suspect that a born male person would always feel an outsider there, even if people were friendly. If I were advising a beloved genderqueer or transwoman student who was interested in the kind of education available at a women’s college, I would suggest a school like Oberlin or Hampshire (or many other similar schools), which have a more open, fluid kind of atmosphere, or a formerly all-women’s school gone coed like Bennington, Skidmore, or Vassar.