Whether you practice a religion or not is pretty well irrelevant (practising Satanists excepted). But it is an area of your life that the social workers will want to enquire into, for purposes of matching you with a child or to investigate possible prejudices you might have. If you apply to some denominational adoption agencies they will not be nearly as strict as they were 20 years ago.
Some religious agencies may be much more rigid about their requirements for prospective adopters, not because they are bigoted but because they have been established for the specific purpose of finding religious homes for children whose birth families want religious homes for them, and to find children for religious families, some of whom need to be sure that children they adopt come from the same religious background as themselves. Some religious communities would not want to adopt (or have their children placed for adoption) across religious boundaries which would be unacceptable in marriage. Religion is an area where birth parents have the right to formally express a preference for an adoptive family. These preferences are not rigidly legally binding, but an agency is required to do its best to respect them.
Many Christian agencies will place children, if not with non-Christians, at least with Christians outside their particular denomination. And many nominally Christian agencies have plenty of non-Christian children on their books for whom they want religious matches, not Christian homes at all. So if you are a member of a non-Christian religion, you should not feel inhibited about applying to Christian agencies; although some will turn you down flat, others will welcome you. And most secular voluntary agencies will also welcome enquiries from non-Christians.
Your political leanings are almost totally irrelevant. I would be very surprised if you were even asked what party you supported or how you voted in the last election; it would probably be illegal to ask and certainly illegal to take your politics into consideration in any way, unless they were so extreme as to bring your suitability as parents into question.
I hope the above has helped you see that agencies’ requirements are, with a very few exceptions, reasonable and flexible, because they are. If you live a normal life in a normal area you have nothing to worry about. Even if you are a little “weird” you can be pretty sure of a sympathetic hearing and consideration by your social worker and the agency.
© Roger Ridley Fenton