Why would early Christians celebrate Passover without the most important aspect of the feast? The apostles in the New testament didn't celebrate Passover because they understood what it stood for. All the feasts pointed to Jesus and Paul especially taught that they were done away with. With Jesus’ death on the cross, the sacrificial system, with all its feasts and festivals came to an end. Paul explains it beautifully in Colossians 2:13-17. This passage explains that the ceremonial law was nailed to the cross. That is, with Jesus’ crucifixion, it was made null and void. For this reason, people can no longer judge God’s people if they do not keep the holy days and Sabbath days of the ceremonial law.
The early Christians would have understood that by keeping the feasts and festivals of the Old Testament, in part or in whole, they would be rejecting Jesus Christ as their Saviour. They would have rejected Him as “the Lamb who takes away the sins of the world” (John 1:29).
So was Paul contradicting himself in I Corinthians 5? No. The Bible does not contradict itself. Obviously the message was different in that chapter and had nothing to do with celebrating passover. If your read the whole chapter its talking about people in that Church who have fornicated. Paul is telling them not to keep company with them. He says, starting from verse 4 "In the name of our Lord Jesus Christ, when ye are gathered together, and my spirit, with the power of our Lord Jesus Christ, To deliver such an one unto Satan for the destruction of the flesh, that the spirit may be saved in the day of the Lord Jesus. Your glorying is not good. Know ye not that a little leaven leaveneth the whole lump? Purge out therefore the old leaven, that ye may be a new lump, as ye are unleavened. For even Christ our passover is sacrificed for us: Therefore let us keep the feast, not with old leaven, neither with the leaven of malice and wickedness; but with the unleavened bread of sincerity and truth." Unleavened bread was bread without yeast. Yeast is used in the Bible as a symbol for sin. Jesus says, “I am the bread of life” (John 6:35), so the unleavened bread symbolized Jesus Christ who was without sin. He explains himslf better in the next verses. "I wrote unto you in an epistle not to company with fornicators: Yet not altogether with the fornicators of this world, or with the covetous, or extortioners, or with idolaters; for then must ye needs go out of the world. But now I have written unto you not to keep company, if any man that is called a brother be a fornicator, or covetous, or an idolater, or a railer, or a drunkard, or an extortioner; with such an one no not to eat. For what have I to do to judge them also that are without? do not ye judge them that are within? But them that are without God judgeth. Therefore put away from among yourselves that wicked person."
In fact Christ instituted the communion service in place of the services that had been a part of the sanctuary service including passover. Luke 22:19-20. "And He took bread, gave thanks and broke it, and gave it to them, saying, "This is My body which is given for you; do this in remembrance of Me." Likewise He also took the cup after supper, saying, "This cup is the new covenant in My blood, which is shed for you." My point is we should only be obedient to God's word. No matter what the intentions were or why the man made traditions were created, they do not count. They are meaningless. When Jesus returns, He will judge us according to His word not human traditions. That is why some will be shocked not to make it to heaven. Matthew 7:21-23, "Not every one that saith unto me, Lord, Lord, shall enter into the kingdom of heaven; but he that doeth the will of my Father which is in heaven. Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works? And then will I profess unto them, I never knew you: depart from me, ye that work iniquity."