In Mark 16:16 and John 3:5, Jesus seems to suggest that we must be baptized to be saved. Is that a correct interpretation of these passages?
The only requirement for salvation is true belief in Jesus Christ as the One who died for sin and rose victoriously over death. Since we reject a works-based salvation, but believe in sola fide—faith alone—we know that baptism is not a requirement for salvation.
Many people throughout the years have been saved on their deathbeds, with no opportunity to be baptized, but they are still saved. The sinner on the cross next to Jesus, who Jesus told would be with Him in Heaven, died before any chance to be baptized, yet Jesus pronounced him saved.
Paul clearly lays out salvation when he told the jailer, “Believe in the Lord Jesus, and you will be saved” (Acts 16:31). He also wrote to the Romans, “If you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved” (Romans 10:9).
To respond directly to the references in the question, Jesus’ interaction Nicodemus in John 3, Jesus contrasts being born of water (literal birth) with being born of the Spirit (salvation). Nothing in this passage speaks of baptism, but being born of the Spirit is the indwelling of the Holy Spirit when a person becomes saved, not anything to do with water baptism.
Its worth noting that the end of Mark—verses 9-20—are disputed as to whether they were written by John Mark in his Gospel, or were added later. Historians and theologians have found some early manuscripts that include these verses, and many that don’t. The ESV translation puts brackets around these verses to indicate that their inclusion in Scripture is disputed.
But even taking these words as an inerrant part of the Bible, the truth of salvation remains the same. Belief is salvation, and baptism is an important symbol of salvation that has been given to us by Christ to symbolize our regeneration with Him.
Baptism symbolizes salvation; faith in Jesus Christ is salvation.