I am not sure snap opinion polls are relevant. Whilst KCIII and Q consort Camilla are not particularly popular, I doubt people would vote, say, in a referendum, to get rid of the monarchy or the church, as its raison d'etre is as 'Defender of the Faith', the 'faith' being that established by the reformation of the church by King Henry VIII. In effect, the Anglican Church was embedded into Parliament at the same time as its foundation as we know it today, in 1559,so a radical reform of the state becoming a secular one ( and it can be done,: see Sweden) and the monarchy being little more than symbolic would entail an entire overhaul of Parliament. OK, so the current government plans to crop a whole bunch of hereditary peers but I can't see it'll take the draconian step of cutting off the CoE from the state as it goes to the heart of the constitution.
If there was a referendum, whilst people might moan about the church and the bishops, I can't see the average Brit voting to get rid of them should there be a referendum as they love all that pomp and circumstance with the Archbishop doing the inaugurations and anointings; the royal 'hatch match and dispatch' carrying on. I can't see that a scandal of this type will dent that cap-doffing forelock tugging stuff, of which the Church plays a key role.