If the policy of MIT or any other institution states that certain spaces are designated as single-sex only, then no, people of the opposite sex do not have the right to use these spaces.
I don't expect people to have a problem with understanding this, in practice. It's really not that difficult to understand what sex you are and where you're allowed to be. Children learn this quite early on.
(Edit: My account is now rate-limited because of downvotes, so I can't reply to any responses. However I would like to point out that if MIT is currently allowing staff and students to use single-sex spaces that are designated for the opposite sex, this is very likely to be a Title IX violation. Unfortunately, sexism is rife in institutions of higher education, and MIT is no exception.)
I don't expect people to have a problem with understanding this, in practice. It's really not that difficult to understand what sex you are and where you're allowed to be. Children learn this quite early on.
(Edit: My account is now rate-limited because of downvotes, so I can't reply to any responses. However I would like to point out that if MIT is currently allowing staff and students to use single-sex spaces that are designated for the opposite sex, this is very likely to be a Title IX violation. Unfortunately, sexism is rife in institutions of higher education, and MIT is no exception.)