Even the Pope acknowledges the other break off faiths like Protestants are Christian for accepting Christ as their savior, they are still break off faiths.
I would still stick to your own Catholic faith since it was what Christ started and He makes no junk.
I wouldn’t worry about trying to understand non-Catholics. Be happy for them if they accepted Christ as their Lord and Savior for their salvation. THAT is where the action is.
Not trying to start a fight here but while claiming the authority of the church, there are current and past Catholic traditions which do not seem to agree with the teachings of Christ and the Apostles.
This is not the place to argue those traditions but keep in mind that nothing is as clear cut as it looks from one vantage point. After all, are you sure that the Authority of the Church did not head east with the Popes of the Orthodox Church. Once again, not the place to argue, just things are not that simple.
Peter was not the first Pope. He couldn’t have been, because he was married. Besides that, he never went to Rome.