does anybody know what religion Robert Stack was?

Not sure about Stack, but it's pretty obvious that the producers of the show had to be Catholic. Almost all the Miracles segments involve some type of Catholic theme.

I thought I remembered reading somewhere that Robert Stack was a devotee of "New Thought," which is kind of a positive-thinking religion found among adherents of the Unity School of Christianity and the United Church of Religious Science. I don't know if the following author knows what he's talking about, but here's what he has to say:

"Among today’s well-known advocates of Science of Mind are actor Robert Stack and singer Della Reese. This 'spiritual philosophy for the New Age' offers a 'specific method by which anyone...may relate consciously to the Creative life Force ['God'] of the universe...for the purpose of achieving whatever constructive objective is desired....Health, abundance, security; love, peace, and happiness are...within the immediate grasp of all who apply...principles...which the Science of Mind explains.'"

http://www.johnankerberg.org/Articles/_PDFArchives/new-age/NA3W1000.pdf

The following indicates Stack participated in the Easter Sunrise service (at least once) at the Hollywood Bowl:

"A multidenominational tone has been a hallmark of the pageant, America's best-known Easter sunrise service. Past services have included a mixture of clergy and celebrities, with Hollywood personalities such as Angie Dickinson, Mickey Rooney and Robert Stack sharing the bowl's stage with religious figures from houses of worship such as the First A.M.E. Church, the Leo Baeck Temple and the Catholic Archdiocese of Los Angeles."

http://www.apologeticsindex.org/news2/an020126-05.html

I don't know how much these articles shed light on Stack's religion, but at least they give us a few clues.