If he's a Ph.D. clinical psychologist and has his state license, it should be no problem for any doctor to accept a letter from him. There are no legal requirements here; as Jaime R D said, it's up to individual providers to decide what their requirements are, not so much for who writes the letter but for what they want to the letter to document. That will also vary according to the type of treatment you're seeking -- what a doc wants to see for surgery will likely be different from what's expected for hormone therapy.
It's terrific that you've found a therapist you feel you can work with, and I hope you're in a position to treat this can as an opportunity for exploration and growth, and not just as a hoop you have to jump through. 🙂