Why doesn’t Mary appear to Protestants?
God can reveal or manifest himself to anyone he chooses in any way he chooses. He can call anyone he wishes to be his instrument. God spoke to Moses in the burning bush. God called and directed Abraham through heavenly messengers. Isaiah was given a vision of an angel touching his lips with a ﬁery coal and a message from heaven.
Jesus spoke from the cross. Later, in a vision of a seraph (angel), Francis received the stigmata - the wounds of Jesus. In later days we believe that God has used his Blessed Mother to call people to conversion and penance through appearances to Saint Bernadette, the children of Fatima and Blessed Juan Diego.
God can reveal himself to believer or unbeliever as suits his purpose. But it does seem more likely that God would choose a person predisposed to accept and act on such a revelation.
Father Adolphe Tanquerey, in his book The Spiritual Life, says that invariably God makes revelations only to those who are already fervent and have already been raised to the mystic state. God usually seems to choose simple, humble and childlike people for his revelations. Perhaps that is because they are more ready to believe and act on what God asks of them. Any vision or apparition is a demand of faith.
Finally, it would be reasonable to suppose that in making a revelation, God would do it in a way that ﬁts the subject’s religious background and mind-set. God would make use of the culture in which the person has been spiritually formed and nourished and would use images and symbols that already have meaning for the subject of the revelation. A Catholic, then, would be more likely than others to accept the Blessed Mother as God’s agent of revelation.