The problem with sorting access into those who are dysphoric or not, yet again, takes no account of the women.
For want of a better word, many women are triggered by men. They don't give a fuck if those men have an illness. In fact if you asked them to give access to men with a mental illness, that could be even worse.
Some women are violently triggered, others are uncomfortable, however much that man thinks access should apply to him. It is very discomforting knowing that the man standing next to you yearns to be you. To the extent that you must accommodate it.
And, of course, gender dysphoria does not give men a pass in terms of behaviour. Karen Jones actually blamed their gender dysphoria for attempting to rape a woman. The fact that they couldn't get an erection, was neither here nor there. The woman said she thought she was going to die.
Jones tied her up, shoved a lemon in her mouth and attempted to rape her. The 'chemical castration' meant fuck all.
There is nothing to suggest that gender dysphoric men commit crime, sexual or otherwise, at a rate less than any other man.