That thinking may feel good, but we can't allow ourselves to settle for anything less than what God commanded. He either made Peter the prince of the apostles (Pope) or He didn't. He either commanded us to eat His flesh and drink His blood or He didn't. He either established baptism as a sacrament or He didn't. These things matter, and you shouldn't be willing to let someone believe erroneous things without offering them correction. We are talking about our eternal resting places, after all. These are conversations that need to happen.
1st sentence: Agreed. "feel good thinking" isn't going to help us--including claiming to be a member of the true church (whether the claim is made through earthly tracking or it is a purely supernatural claim). If we don't genuinely have a connection to God through Jesus Christ, we won't go where we think we are. Jesus made that abundantly clear in numerous places, including Revelation 2 & 3, Matt 7:21-27, and Matthew 25, for instance.
2nd sentence: Jesus never said Peter was the prince of the apostles or pope. In Scriptural facts, Jesus said many things with regard to Peter, including Matthew 16 where He both said "Upon this rock, I will build my church..." and "Get behind me satan, you are an offense unnto me; for you savor not the things that be of God, but those that be of men." Later in Scripture, Jesus says to Peter: "
Luke 22:31-32 "Simon, Simon, Satan has asked to sift all of you as wheat. But I have prayed for you, Simon, that your faith may not fail. And when you have turned back, strengthen your brothers." Peter is restored by Jesus. He certainly takes a leadership role; but not the way that people bow to your pope today. In fact, in Acts 11, Peter was challenged by the believers of the circumcision (Acts 11). Later in Acts 15, it at least appears as though James is leading the Jerusalem Council, not Peter. Peter was so clear that it wasn't about him, that despite Paul calling him out for playing the hypocrite (in Scripture), Peter declares that Paul's writings are to be considered Scripture (in Scripture).
If your church is truly descendant from Peter, where is the power that Peter, Paul, Stephen, Philip, and others walked in?
3rd Sentence: "Then Jesus said unto them, Verily, verily, I say unto you, Except ye eat the flesh of the Son of man, and drink his blood, ye have no life in you" during a longer section where He was offending the Jews present and during a time He, by His Words, chased away most of His disciples. (John 6). Later, Jesus "Took bread, and blessed it, and broke it, and gave it to the disciples, and said: 'take, eat, this is My Body.' and he took the cup, and gave thanks, and gave it to them, saying, 'Drink ye all of it; for this is My Blood of the New Testament, which is shed for many for the remission of sins." (Matt 26:26-28 and Mark 14:22-24). In Luke 22:17-20, He adds "Do this in remembrance of me" related to taking of the bread. Paul shares the fullest account in 1 Cor 11:23-34. When we partake, it is certainly more than just eating bread and drinking of the fruit of the vine in God's sight.
4th sentence: Baptism, according to the Scriptures isn't an option. The Apostles and Deacons baptized when someone declared belief. It wasn't about pomp and circumstance, it was an act of obedience to God. Again, Cornelius comes to mind: "While Peter yet spake these words, the Holy Ghost fell on all them that heard the word. And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God. Then answered Peter, 'Can any man forbid water, that these should not be baptized, which have received the Holy Ghost as well as we?' And he commanded them to be baptized in the name of the Lord." (Acts 10:44-48).
If Peter recognized people who the Holy Spirit fell on, but who certainly were not of their group, and your church truly descends from Peter, why do you reject those who God is clearly working through today, because they aren't part of your church?