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.)
Nonetheless, even in cases where someone has managed to somewhat disguise themselves as the opposite sex - or think they have done so - they will still be expected to respect boundaries, and stay out of spaces designated for the opposite sex.
I see the Supreme Court ruling as striking just about the right balance in law. It affirms single-sex spaces as actually being single-sex, and confirms that both sex and "gender reassignment" are protected characteristics in the Equality Act. So sex-based rights are upheld and at the same time there are protections against discrimination for the trans-identified.
As an example of how this should work going forward: a male work colleague who decides to start calling himself a woman and putting "she/her" in his email signature and so on can't be discriminated against because of this, which is fair. But also his female colleagues can be assured he has no right to start barging in on the women's toilets or changing rooms, which is also fair.
Back on the topic of boycotting Netflix, I personally think it's an overreaction. The whole gender identity ideological system sits somewhere between ludicrous and sexist, depending on exactly which beliefs someone takes from it, but there's loads of other shows on Netflix that are also ludicrous and also sexist. I feel it's an opportunity for critique of these ideas, rather than a blanket boycott of the whole platform.
That said, I wouldn't want my child to start believing this nonsense when she gets older but it feels like a fad that's on its way out. I don't think it'll be a problem. I'm more concerned about all the other misogynistic messaging that shows no sign of disappearing any time soon.
Not really though. This is about female and male, not feminine and masculine.
Like for example, women in prison won't have any problem if they don't look stereotypically feminine. But they certainly are under significant threat if male prisoners are locked up with them.
But that report misses the point that women's rights to single-sex spaces is about boundaries, consent and protection from male presence in intimate settings. By only surveying "transgender experiences" it's basically just ignoring women who object to this and implying that women's boundaries and consent don't matter.
Looking at crime statistics won't capture the discomfort and intimidation that many women will experience upon encountering intrusive males in female spaces, nor their withdrawal from public life as a consequence of this.
Also it focuses heavily on toilet facilities but this is just a part of the wider issue. Like for example there's a much worse problem in women's prisons where males are being transferred in based on self-declared gender identity, with sexual assaults, rapes and impregnation of female prisoners by these men occurring as a direct result of such policy.
It was May's plan to introduce gender self-ID that galvanised such a strong and rapid response against it, largely coordinated on Mumsnet, within its Feminism and Women's Rights (FWR) subforum.
In fact, the recent UK Supreme Court case which resulted in a ruling that references to "sex", "woman" and "man" in the Equality Act refer to biological sex (as in, a person's sex observed at birth), was brought by a small group of women who met on FWR.
More generally, I think much of the reason that the UK has been so successful in resisting and reversing policy that prioritises self-declared gender identity over sex is that we have a strong tradition of women's advocacy for single-sex provisions, that has been pursued regardless of other political affiliations.