St. Peter went to a synagogue. So did the other 1st century Popes...
But what about the 2nd and 3rd and 4th and 5th and 6th and 7th and 8th and 9th and 10th and 11th and 12th and 13th and 14th and 15th and 16th and 17th and 18th and 19th centuries?
So did St. Paul, but that was different than today. First, nowhere in the NT is there any indication that anyone prayed to Jesus before or after the Resurrection. The followers of Christ were Jews, religiously and otherwise. Christianity was an offshoot of Judaism the way Samaritan form of Judaism is to this day.
But, by the end of the first century, Judaism and Christianity became irreconcilably divergent and separate religions. This was not the case before or immediately after the Crucifixion.
After Jamnia, in the '90s of the first century, Jews added a daily prayer known as Birkat Ha Minim (against heretics), which is euphemistically called the "12th blessing"—basically a curse of the sectarians, specifically the Gnostics and the Nazarenes, or Christians).
The Pope, or any Christian, has no business praying in a place where Jesus' followers are cursed daily, and where God is implored to destroy them. Ironically, the Muslims show more reverence for Jesus (as a prophet) and even his blessed Mother, for whom they have very deep affection.