I have a few vintage readers in my collection that were created for the religious market. Two little primers that were published by Westminister Press for an organization called Christian Faith and Life. These little books were designed to be used at home, or in Sunday School, so weren't technically school books. However, it's possible they were used in Christian schools during that time. They were published in the late 1950s.
I also have two editions of Scott, Foresman's Cathedral Readers. (Scott Foresman published the Dick and Jane books, and were the largest elementary school text publisher of the day). The Cathedral Readers were designed for the Catholic school market. They were nearly identical with their non-parochial school counterparts, except for the stories about religious themes. It's kind of fun to see the cute little reader illustrations with a priest or nun in them. I'm sure for Catholic school kids they seem perfectly ordinary, but to me, they are quite novel! My Cathedral Readers were published in 1947 and 1964.