Like others said, the answer is more like "depends what do you want to know". In this case, you need to figure out what is the point of an all-female college at all. Fixing systemic disadvantages? Rape safety? More cooperative athmosphere? What you need to figure out is not whether trans women are "really, truly, indeed" women, which is a meaningless kind of sentence, but more like whether they can be categorized as women for the purposes of the goals of an all-women college.
But another relevant aspect is, and this I guess is not discussed so much on LW so I am not really sure what is the best way of wording it... basically that means to an end tend to ossify into values in themselves, via becoming part of identity, tradition etc. There is the old story of a Zen monastery, where the cat made a lot of noise during meditation so they ended up tying it up and 200 years they write treatises about the spiritial significance of having a tied up cat around symbolizing the tied up mind.
Even if the idea of an all-women college was originally utilitarian, a means to an end, now it is easily identity based. And identity isn't a rational thing. There is no truly objective answer whether biological women should or should not accept trans women into their idea of women-as-an-identity-group, because identity is something that tends to break free from the original reasons of creating it. People tend to ask precisely these "are X truly, really, indeed Y" when discussing identity, and there is no good answer, because on the rational level we can only ask the question "is it useful to categorize X as Y for the purposes of Z" and identity is precisely something that breaks free of such purposes and becomes a tribe on its own. There is no right or wrong answer about who should be allowed to be a member of a tribe. It is largely based on the feelings of the other tribe members. You cannot really give an objective, rational answer to who should be considered a hardcore Manchaster United fan or what is true, real punk music as opposed to pop punk. This just based on how the people in question feel.
This thread is for asking any questions that might seem obvious, tangential, silly or what-have-you. Don't be shy, everyone has holes in their knowledge, though the fewer and the smaller we can make them, the better.
Please be respectful of other people's admitting ignorance and don't mock them for it, as they're doing a noble thing.
To any future monthly posters of SQ threads, please remember to add the "stupid_questions" tag.