Please pick an appropriate book from that list and report a summary of what it says on the OP’s question.
Nah. The op was asking not only who it was who did not go but
The answer to that question is yes, by using classic methods that historians use, and for those of us who are not historians by looking up their work, which exists.
It is not unknowable.
FWIW someone actually intrigued by the question can get a Kindle copy of the second, which sounds promising, for under $16 …
The OP request for demographics is slightly answered, albeit obliquely, and FWIW, in an article about that second book. Not directly who did not go to church regularly then, but where the big increase was anyway. Suburbia. And supply side driven.
He characterizes the decade’s thriving organized religion as a supply-side phenomenon, in which suburbanites could almost always find a church of their denomination close by.
So “Build it and they will did come.”?
To Kingdom Come. 
Note that Dad in that picture has two tufts of hair on either side of his head, is wearing red, and has smoke hanging over him. Clearly, Satanic!