Prisoners are usually assigned based on the legal gender classification. Due to the complexity of these cases, each case tends to be looked at individually and the inmate moved to either a wing or area of the prison for the vulnerable/dangerous to be isolated from other prisoners and to undergo closer surveillance or in special cases, moved to an alternative prison.
Moving to a female prison is not possible based on what you identify with, the decision is based on the safety of the inmates on a case by case basis and very rarely happens. Regardless of what this inmate identifies with or their orientation is, they would be considered unsafe as well as be unsafe in a female prison.
The inmate is claiming that rights i violated due to not having access to the same facilities as other prisoners, which is unsurprising given their isolation.
The person is a total nut-job, everything i read online about this person prior to the self mutilation, points to mental instability. This person requires significant psychiatric help and likely more than what the prison can offer. Unfortunate but true. The only solution i can think off is moving this person to a facility more catered to the mentally ill but this could put other people in danger as well as not give them access to the facilities which was refused the inmate and therefore caused the self harm.
This specific case is particularly interesting because though the wing designed to house vulnerable prisoners has facilities the inmate wants, it also house the prison population they are a danger to (paedos and such) but unfortunately the normal part of the prison is a danger to them due to how they present themselves and confront those who dont accept the inmates identification.
The situation very much reminds me of the riddle with the Grain, Goat and a wolf required to cross a river, except this issue is made worse that leaving any combination of prisoners (the inmate, general prisoners and vulnerable prisoners) in the same place will likely put those parties in danger.