Is it the Pope’s Private Opinion that Muslims Worship the Same God?

No. The Second Vatican Council taught that Muslims worship the one true God:

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. (Nostra Aetate 3)