Years ago I was in the care of a Jewish psychiatrist and a Catholic therapist at the same time for a severe clinical depression. The Catholic therapist was good, but we didn’t really get into religion that much, but he was a very good therapist. The Jewish psychiatrist was fantastic, supported me in my spiritual efforts, encouraged me to continue in my religious practice, and was very careful about medication, explaining the effects to be expected, side effects, etc. I never felt overmedicated. He also obtained a careful health history. He never tried to force anything on me, or make me feel as if I were a less than an intelligent person incapable of making decisions about my care. He was always respectful of me, and as I said, supported me in my spirituality, although he did not give religious advice. And he was a good listener.
I think, that when choosing a therapist, the most important thing is their ability to listen and adapt their therapy to the person as an individual, rather than just using textbook techniques. They need to see you as an individual and support your values. Just being Catholic or a Catholic therapist does not guarantee you will get the best care, or that the therapist is the right one for you. Sometimes you have to look around.