Who typically did NOT go to church in the 1950s?

Nope. Those numbers, admittedly cited almost everywhere, are from Gallup, which has been asking the question since the 1930s. Well, a question, but not exactly this one. As shown in that link, the actual question was “Did you, yourself, happen to attend church, synagogue, or mosque in the last seven days, or not?”

I can think of a myriad of reasons why an individual, even a dedicated, deeply religious believer, might miss the the most recent weekly service. The implication is that the Gallup percentage is lower, perhaps much lower, than a question asking whether a person or their family regularly attended services. What that percentage is becomes difficult to know. This site claims " During the 1950s and 1960s, nearly 70% of Americans identified as regular churchgoers, attending services every week." [bold in original] No source is given, but it backs up my contention and is the only stat I could find.

Religion has never been a universal in America. It unquestionably dominated the early years and peer pressure was strong in small towns. As the country urbanized, non-attendance became less visible and so went less challenged. Attendance is not the same as belief; modern studies say that overall religious affiliation is about the same in urban and rural communities.

I’m not sure much more explanation is needed.