1.Some of it could be because religious viewers have segregated themselves with religious themed television networks. To be sure, I don't know that these stations do any drama or comedy programs, but there is religious television.
2.Prior to Cable television starting sometime in the 1970s, there were initially just two major networks (NBC and CBS) and two smaller networks (ABC and Dumont) and in bigger cities an independent television station. (It was these independent stations that carried syndicated programs like The Adventures of Superman, the first hit syndicated program.)
During this time, from 1955-1956 there was a highly regarded religious themed show that aired on ABC called 'Crossroads.'
https://en.wikipedia.org/wiki/Crossroads_(1955_TV_series)
Many of the episodes are available on Youtube
https://www.youtube.com/watch?v=UDWi_wTtu9w&list=PLTKmp3L0wn-VajWnU7rfwklcKAfHxtgjW&index=23.Similar to Crossroads in being an anthology series was the program that was initially called The Fisher Family that aired on the Dumont Network and then on ABC from 1952-1956. It then became known as This is the Life with new episodes airing in syndication on independent television stations and ran until 1988, I believe on a religious themed network.
4.I'm not sure about the 1960s in terms of new explicit religious themed shows, but many Westerns in the 1950s and shows like The Twilight Zone and Star Trek in the 1960s certainly implicitly touched on many religious themes.
There have been more recent explicitly religious shows. In the 1970s Little House on the Prairies was a popular show although in many ways it essentially became a parody of itself as it became little more than a 'what disaster can befall the family this week?' spectacle.
Also in the 1970s though, the show MASH featured Father Mulcahey who was treated with respect and reverence.
In the 1980s, Michael Landon who starred in Little House on the Prairies came back with Highway to Heaven.
In the 1990s there was Touched by an Angel, a rather straightforward show about Angels providing miracles, and, on the other side, a more complex show that was both praised and criticized by organized religion called Nothing Sacred that was created and developed by a Jesuit Priest.
In the 2000, continuing in that more religious but sometimes critical of organized religion theme was Joan of Arcadia.
This is not an exhaustive list of all explicit religious themed drama programs that have aired on network television, but it is many of the main ones.
1.Crossroads
2.The Fisher Family/This is the Life
3.Little House on the Prairies
4.Highway to Heaven
5.Touched by an Angel
6.Nothing Sacred
7.Joan of Arcadia
I'm not familiar with many new programs after the early 2000s and I know nothing about cable or streaming programs.