I do think Mad Men has a bit more discussion of religion than perhaps you're giving it credit for--I'm thinking in particular of the storyline in the 2nd season with Peggy and Colin Hanks. It's fairly clear that Peggy rejects the strict mores and guilt of the Church to a fairly large extent, but she's still influenced enough by Father Gil's suggestion of confession to admit her baby out of wedlock to Pete, even as she rebukes him. There's also of course fairly frequent discussion of Jewishness, though of course a lot of that comes through in a non-religious context.
Still, it's fair to say that Mad Men's not a super religiously attuned show--which in a lot of ways reflects the particular slice of society the show samples--famously secular and non-Protestant New York before the Fourth Great Awakening really picked up speed.
These are good points. Religion is not completely ignored by Mad Men, although it's notable that it focuses on the same Catholicism/Judaism/Western Buddhism triad that I describe with respect to The Sopranos.
Don Draper also has that great moment in the final season when he sees the devil in the engineer who comes in to install the firm's new computer. Admittedly, the thrust of this scene is that Don is having a drunken outburst, but the form it takes is significant.
Maybe it's my own biases speaking, but I view this as one of the most important moments in the series and particularly crucial to the moment of revelation at the end in which he conceives of the Buy the World a Coke campaign. Don understands the cold and mechanized Tower of Babel that we are building for ourselves and the allure of offering an escape from that in something human.
I think the Catholic/Judaism/Western Buddhism aspect, as shared with the Sopranos, is mostly a side effect of the Tri-State area setting, though unlike
the Sopranos Mad Men does of course have lots of WASP or North European characters who'd theoretically be Protestant. Though it's fairly realistic in showing most of those characters as thoroughly secularized.
It's been a minute since I've seen the back half of Mad Men to be honest, which I watched when it was airing while I was in High School and haven't rewatched since. I'm currently rewatching (early Season 3) and will probably come back to this thread once I get to that scene.