Most agencies/countries won't let you adopt if you're too old. (35 is usually the cutoff).
I do recall a religious test for one agency - and I think (don't quote me on this) it was Catholic Charities. I believe they only accepted Catholic prospective parents. But please don't take this as gospel, it's been many years. I'll look it up and post it, if I can find it.
Our friends in VA, Baptist pastor and his wife, are adopting through Catholic Charities. They said CC was the most supportive and helpful of all the agencies they contacted. They are in their 40's and have some health problems, so thought they would be unable to adopt at all.
Catholic Social Services requires that only one of the parents be Catholic.