I genuinely believe the marriage controversy had very little to do with it - I mean, after the rural purge CBS was kind of courting "controversy" with the Norman Lear shows. It also aired in the same season where Maude had an abortion, so CBS was at that point not trying to be a conservative network even if it's what it's mostly known as today.
TvObscurities actually has a good archive of the 1972-73 ratings. Here's the night where the series finale aired:
All in the Family: 34.0/54
Bridget Loves Bernie: 21.5/33
Mary Tyler Moore: 25.6/41
Bob Newhart: 23.6/33
So by the end of the run, it had cratered to the point Mary Tyler Moore and Bob Newhart was out-rating it. The whole "religious groups got it cancelled" is a good story, but it is just that.
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te. ·