Women's Hour has regularly hosted debate from both sides - but must remain impartial as BBC. Presenters, again, must refrain from giving their personal opinions. The media in general is worried by speaking out on this.
Women's refuges have in practice for many years welcomed and supported trans women - as is the case with public bathrooms, women's groups and pretty much everywhere in 'civilised' society. Because the numbers are small, it's been on a case-by-case basis, I guess. Most women have no issue with trans people, and are quite happy to treat them as the gender they wish to present as on an individual basis. I know I am.
The issue is that if it becomes de-medicalised entirely - that anyone can say they are anything - and that becomes enshrined in law, it will open up a very difficult, unprecedented situation. A women's rape shelter won't be ABLE to turn away a man presenting as a women to gain access for whatever reason - even if it seems suspicious and a detriment to their core users.
The trans activists say this is hysterical talk, catastrophising - that all trans people want is the peaceable right to go about their lives not being discriminated against. But not all men who want to present as a woman are doing it for those reasons - some of them will be doing it for nefarious purposes. And if you take away the legal hoops that need to be jumped through, it becomes much easier for people with bad intentions to exploit others.
I don't see why needing 2 medical opinions that you do suffer from gender dysphoria, and the reasonable expectation that you've made steps to live fully in your chosen gender for 2 years, needs to change. And no one can seem to give a nuanced argument on that, other than that the process is 'traumatic'.