A number of years ago, the faithful were seriously struggling. Word had gotten out that the Pope had said a number of things, in public even, that were an apparent denial of the faith. Some wondered whether the Church could survive this. Some questioned whether he should have ever been chosen as the Pope. Many murmured and gossiped about him. Quite a few were angry at him, for they knew that unbelievers had heard about it and it brought shame to the Church. Some prayed for him, but there were doubts in their hearts when they did. It was a very hard time.
The Church got through it, however, because Pope Peter was the one chosen by God as the first Pope (since that is who is referred to in the paragraph above). Yes, I am speculating about how people dealt with Peter's denial of Jesus on the night of His arrest. I am also speculating about how St. Peter had to be rebuked by St. Paul. I am not speculating, however, that people struggle with Popes. They struggle when a Pope says something they do not like. They struggle when Popes sin (and, yes, they do). That is not new (obviously); it is a part of what it means to trust God to work through fallen and sinful men to lead His Church.
So, whether it is Pope St. Peter, Pope Benedict IX, Pope Leo X, Pope John XII, Pope Pius X, or Pope Francis, God is always the One in charge, and it is in Him that we are to place our hope. Good Popes and bad Popes come and go (and we have had both) and God knows what He is doing. Yes, good Popes can do wonderful things for the Church, but even bad Popes can be used by God for the good of the Church (we may not always see that good, but God's love is what decides what He sends our way). Let us always keep our hope in Christ; good Pope, bad Pope, it does not matter -- His Church will endure until the end of time.