Apostle Paul spoke to the Corinthians in a very Jewish way: “For Christ, our Passover also has been sacrificed. Therefore, let us celebrate the feast, not with old leaven, nor with the leaven of malice and wickedness, but with the unleavened bread of sincerity and truth.” (1 Cor 5:7-8). Did the Corinthians truly celebrate Passover? Did they even understand what Paul was trying to say by calling Jesus a Passover offering? The assembly of Christ-followers at Corinth had many former pagans, but many were God-fearers of Israel's God. It appears they knew about Passover and its meaning. Otherwise, the apostle’s words would have been meaningless to them.
Corinthian believers were most likely familiar with the Exodus story and understood how Messiah’s sacrifice provided Exodus-like redemption. The teacher’s words were not intended to encourage them to go celebrate Passover as other Jews did in a literal way necessarily (at least this was not the point!). Rather, Paul used Passover as a symbol, as an illustration, of how purity was a serious and crucial concern that the Corinthians neglected.
In a broader context, Paul told his disciples to expel those who sinned continually from their midst. Just as Jews removed leaven before Passover and mixed a new batch of dough without fermentation for the feast, so should the Corinthians seek to be a new and unleavened or sinless lump. They should clean out their leaven and expel sin from their gatherings. In Paul’s Jewish view partaking of Christ is like eating the Passover offering in Jerusalem. It can be done only in purity or not be done at all.