Answer

The idea that Muslims worship the one true God is not a "private opinion of popes." It was the teaching of Vatican II in its document Nostra Aetate:

The Church regards with esteem also the Muslims. They adore the one God, living and subsisting in himself; merciful and all-powerful, the Creator of heaven and earth, who has spoken to men; they take pains to submit wholeheartedly to even his inscrutable decrees, just as Abraham, with whom the faith of Islam takes pleasure in linking itself, submitted to God. (NA 3)