Can non-Catholics be saved? What about people who never heard of Jesus?

Two truths held together.

First: "Outside the Church there is no salvation." All salvation comes from Christ through His Body, the Church. "Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation" (Lumen Gentium 14; CCC 846). Jesus is "the way, the truth, and the life; no one comes to the Father except through me" (Jn 14:6).

Second: "This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church" (CCC 847). "Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience, those too may achieve eternal salvation" (Lumen Gentium 16).

How this fits. Such people are saved by Christ and through the Church, even without knowing it, because God is not bound by His sacraments though we are (CCC 1257). What is condemned is rejecting the Church knowing it to be true: "Those could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it" (Lumen Gentium 14).

Other Christians. Baptized non-Catholics are truly Christians, "in a certain, although imperfect, communion with the Catholic Church" (CCC 838). Their Baptism is valid; the Spirit works in their communities. But the fullness of the means of salvation exists only in the Catholic Church (Unitatis Redintegratio 3; Dominus Iesus 16-17).

Other religions. The Church "rejects nothing that is true and holy" in them (Nostra Aetate 2), while teaching that they are not equal paths to God and contain errors alongside truths. Religious relativism, the idea that all religions are the same, is explicitly rejected (Dominus Iesus 22).

So why evangelize? Because knowing Christ is infinitely better than not knowing Him, because invincible ignorance is much rarer than we assume, and because Jesus commanded it (Mt 28:19). The possibility of salvation for others is a reason for hope, not for silence.