Trans women should be in women's prisons because they are women
Well, the law doesn't necessarily support this: here's the expert opinion of Prof. Rosa Freedman (expert in international human rights law) to a recent House of Commons Select Committee, on whether transwomen are women:
In law, it says that a man is someone who is born male with biology in terms of chromosomes, gonads and genitalia, and a woman is someone who is born female with the same biological factors. Now, there is the legal fiction where a trans woman or a trans man may gain a gender recognition certificate that changes their legal sex but does not change their actual sex. Currently, in law, a trans woman is a trans woman unless she holds a GRC, in which case she is male, she is a trans woman, but, legally, she would be recognised as a woman for many but not all purposes.
That sounds complicated because the law is currently in a bit of a mess and that is why we need to change and streamline it. My opinion, therefore, changes depending on whether someone holds a GRC, but I stick in line with what the law currently says, which is that your sex is determined by biology.
The GRC confers the 'legal fiction' that a transitioned man (a transwoman) is a woman, and admissable to single-sex spaces, except where she is excluded as a proportionate means to achieve a legitimate purpose. Hospital single-sex wards, single-sex prisons, women's refuges, women's rape crisis services, and places such as public changing rooms and lavatories are all examples of single-sex services/places covered by this legal preservation of single-sex spaces.