I might not be back to post here, if this thread doesn't actually lift its game up. I hope this'll help, anyway.
1. Women still face many challenges that men don't. This is still a big issue in our society, and ought to be eradicated. Yeah, patriarchy (institutional power structures favouring men) is a thing, and is a big cause of these issues. If you truly believe that women are afforded an equal opportunity as men, you're only kidding yourself.
The point about women not being strictly legally disadvantaged is irrelevant. A society can treat a group extremely inequitably, whilst affording them the same legal rights and duties. These cultural issues, in some ways, are even harder to address than the legal inequalities -- they're not written on a piece of paper.
2. Feminism is a movement. You don't have to agree with every single thing that every single person associated with this movement does to recognise its importance. That does not mean, however, that you should criticise campaigns simply because they remind you of those challenges that women face (e.g. the cupcake stuff).
3. Even completely ignoring the (quite frankly necessary) context of it, a women's room obviously is desired by many women-identifying students (see: many of the women posters on this thread), and so it is quite beneficial, to say the least. On the other hand, those opposing it are yet to actually come up with a single example of actual harm caused by it. Hence, there is absolutely no reason to do away with it. It seems to me like the reason they're opposed is that mentioned in #2 above.
4. I think it'd be wise to agree to treat violence of any sort (and particularly, relevantly to this discussion, sexual and domestic) as extremely serious issues, and not try to use them for point-scoring. Victims (of both genders) require support, and for society to do its best to ensure that there are as few future victims as possible. Those issues of course aren't independent of gender, but I think those are important guidelines to stick by.