At first glance, I don't believe that convicts should get government-funded SRS when non-convicts can't, although convicts paying their own out-of-pocket or insurance monies to get SRS provided to them within the prison medical system would be reasonable; then again, I'll admit to not knowing diddly squat about the prison medical system. At second glance, however, it does complicate things that prisoners are essentially receiving government-funded living in the first place; that's the tradeoff that we make as taxpayers and citizens when we decide to fund a prison system in the first place. If we would provide other healthcare to prisoners - which I believe we do - then we should provide SRS as well.
I do strenuously object to the original post's unjust characterization of prisoners as vile people. Certainly some are, but crimes are committed by a wide variety of people for a wide variety of reasons, and a guilty convict's crimes may range from a cold-hearted, premeditated murder for financial gain to an emotional, spur-of-the-moment retaliatory murder of a violently abusive spouse, to financial crimes, committing thefts and break-ins out of desperate poverty and hopelessness, etc. Inevitably, some percentage of convicts are wrongfully convicted, as well; our justice system is not infallible by any means. It should also be acknowledged that the culture of prisons increases the likelihood of recidivism, and can make people into real, hardened criminals who may not have been before; prison life is very dangerous, and provides enormous short-term incentives in terms of safety in numbers for prisoners to become involved in gangs and other activity that leads to further violence and crime. Ultimately, a more reform- and societal reintegration-minded prison system, designed to fight back against this dangerous gang culture and provide alternative avenues towards education and gainful employment, would be the best thing for all prisoners, transgender and otherwise.
It doesn't seem wise to me to simply punish convicts when such a mentality simply makes it more likely that when they're released, they'll commit more crimes, hurt more innocent people, and end up in prison again. Let us not forget that it is extraordinarily expensive to keep people in prison, as well as being demeaning and tending to turn people towards a career criminal lifestyle; imprisonment is extraordinarily expensive in both financial and human cost, and should not be undertaken lightly.
This issue basically touches on the deeper need for prison reform; it's not as simple as it may appear at first glance.