The first therapist I went to see was part of a group called Pastoral Counseling. Although most of the counselors were ministers and rabbis, the counseling did not revolve around religion in the least, or even spirituality.
The good part is they calculate counseling fees on a sliding scale. The great part is that some of the best counseling I've gotten has been from that guy and, later on, a friend who also happened to be a pastor with a background in psychological therapy. The not-so-great part is that I had to arm-wrestle that first therapist to write a recommendation for me to apply for an NIMH study. But then, that was about 25 years ago...
~ jr