My wife and I adopted through CPS in Dallas, TX. As atheists, we had about 2 or 3 agencies to choose from that were not of a religious affiliation. That is out of a list of about 50 agencies. Once we completed our training, background check and the like, we had our home visit. This included questions like, "how will you provide for your child's religious upbringing?", and the basic, "what church do you go to and how often?". We ended up adopting a 2 and 12 year old. The foster home they had been in for 1 1/2 years was Pentacostal, and during our one visit to see their church, there was speaking in tongues, laying of hands, and open statements of racism and homophobia.
What is the point of this background? Religion is a part of our society, and moreso when it comes to adoption. Your main objective, I assume, is to adopt a child. With that in mind, there should be no problem finding a non-religious or lightly religious organization to work with. There aren't many, but they do exist. It is a little less likely if you are adopting an infant through private adoption, but they are out there. Start by contacting CPS and going to an introductory meeting. Its the first step of adopting through CPS. Even if you don't want to go that route, they provide a long list of adoption agencies, and you can research them to find out if it is a good match. If you are in the DFW area, the one I can recommend is Gladney. Just Google them, and you can get some more information.
Hope this helps. Good luck. It isn't an easy path, and we found we usually had to keep our opinions to ourselves, smile and nod, and come up with some very nice sounding, vague answers to religious questions. One solution: check out the Unitarian Church. That way you can say you go to a church without lying. :)