I agree with you that the original wording should have rigorously ensured common knowledge among the islanders of their logicality and devoutness, since common

I agree with you that the original wording should have rigorously ensured common knowledge among the islanders of their logicality and devoutness, since common knowledge (of a different fact) is what the puzzle is about. But that's a subtle point and not the source of the previous disagreements here.