Our potential birthmom said one of the reasons that she picked us was that we did NOT go to church every Sunday. Also, another PBM that I had a nice conversation with said more or less the same thing. Both women were from the Bible belt, both were spiritual but not practicing. They responded to our independent outreach (webpage that we did independent of our agency webpage).
The agency that we also did outreach with is part of Jewish Family Services, but we are not Jewish. They are just affiliated with them, but work with families of all kinds of faith, sexual orientation, singles, etc. There are so many options out there you should have no problem finding a professional to work with (agency, attorney, or facilitator).