Are Catholics obliged to believe in any apparitions of Jesus, Mary, or the saints? Is that necessary for a person’s salvation?
Excepting the apparitions of Jesus recorded in the New Testament, no. You could deny that Jesus appeared to St. Margaret Mary Alacoque (devotion to the Sacred Heart), or that Mary appeared to Sts. Bernadette Soubirous (Lourdes), Juan Diego (Tepayec), or anyone else. Why? These are private revelations—no matter how well publicized. Believing in a private revelation cannot be a requirement for salvation. Scripture is the best example of public revelation.
The examples cited above all have feast days approved by the worldwide Church. It would be foolish to challenge them, but it would not imperil someone’s salvation.
The private/public revelation distinction enables the Catholic Church to decline recognition of highly doubtful apparitions reported in Bayside (New York), Necedah (Wisconsin), Garabandal (Spain), or many other places.