Are you really suggesting the Anglican vote was more significant than labour voter shift in red wall seats?
Done a little bit of digging around this.
Imagine anglicans didn't vote 58% tory (as suggested in the survey) but at the same level as non religious people (32%). That would result in a reduction of 4% in the tory vote and an increase of 4% in the vote of other parties. So that means that any seat where the tories won by less than 8% would quite likely have been lost.
So the tories gained 58 seats at the 2019 election, many of those from Labour in the 'red wall'. However in 36 the winning margin was small enough that had anglicans voted as non religious people did then they would not have been won by the tories.
So that takes the tory majority down from 80 to just 8. Ah you say, still a tory majority, albeit a tiny one.
But of course you need to go further - there were some seats which the tories retained with a small majority (often in more 'remains' areas) which they would have lost with a reduction of their vote share of 4%, balanced by gains by other parties. Good examples being:
Wimbledon (retained by the tories with just 628 majority)
Cheltenham (retained by the tories with just 981 majority)
Winchester (retained by the tories with just 985 majority)
Chipping Barnet (retained by the tories with just 1212 majority)
Failing to retain just those four and majority is gone - and there are a fair few others that would likely not have been retained had anglicans not voted 58% tory, but 32% tory as per non religious people.