A short blog with a short answer....No Christians Do Not.
New Covenant Christians have the sacrifice and shed blood of Jesus Christ as their passover. It was done once for all by the Son of God on the cross. All you need to do is accept Him as your savior, be baptized in the name of the Father, The Son, and The Holy Spirit, and you will receive the Holy Spirit. Salvation is through Grace and Faith in Christ, not through laws.
Christ fulfilled and ended the requirements of the Old Covenant completely (Colossians 2:14, Ephesians 2:15). Jesus explained what He did in Luke 24:44 to His disciples after His crucifixion and resurrection from the dead. In this He explains what he told them earlier in Matthew 5:17-18, that He came not to destroy the Law and the Prophets, but to Fulfill them, which He did. In Matthew 11:13 Christ also explained that the Law and the Prophets were only prophecy until John the Baptist, until, not afterward.
There is no requirement to keep the Old Testament Festivals or any of the other commandments contained in statutes and ordinances including the upcoming Passover and Days of Unleavened Bread.
Today the fulfillment of the Commandments of our Lord is the Christian requirement. He commanded us to, "Love one another as I have Loved You." John 15:10 " If you keep My commandments you will abide in My love, just as I have kept My Father's commandments and abide in His love."
His Father's commandments that he kept and the ones that He commanded us to keep are not entirely the same. They are different as He says. In verse 12 Christ gives us His commandments, "that you love one another as I have loved you." Christ repeats the same commandment in verse 17.
Christ gave the commandment to us in John 13:43, 14:15,21. "He who has My commandments and keeps them, it is he who loves Me." said Jesus.
What about a communion service with the symbols of the new covenant recorded in Luke 22, Matthew 26 and Mark 14 with the bread and wine? Once a year or several times, as long as bread and wine are taken in a reverent manner as a memorial of Christs sacrifice. Only in I Corinthians 11:26 is any frequency attached to this ritual of remembrance, and Paul simply states, "For as often as you eat this bread and drink this cup you proclaim the Lord's death till He comes. And the occasion is not the Lords Supper being recorded in this passage, only a potluck type meal in this church that experienced a degree of disharmony.
With the Passover being fulfilled on the 15th of Nissan with Christ's death on the cross there is no longer a reason to observe this event in an old covenant fashion while under the new covenant. Christ was the end of the Law of Moses, the end of the old covenant (Romans 10:4). The date and ritual became obsolete. Heb 8:13, "He has made the first obsolete.
In the New Covenant we fulfill the Whole Law by Loving your neighbor as your self.
However, If you think that is easy, think again. Christ's command not only included treating others as you want to be treated, but goes far beyond that....Christ died for you and for me.