The popular opinion seems to be that salvation is assured to all, except to the worse criminals. But, what constitutes a crime? It is also unclear as it changes with the culture. Abortion, adultery and sodomy are no longer considered crimes and therefore are not believed to lead to damnation. Smoking and disposing of animals are among the new crimes.
In the West, most Christians are not different to others in their moral behavior. They think that only fanatics would adhere to divinely ordained moral principles. Therefore they are not necessary for salvation.
Saint Paul teaches that salvation is a gift that comes through faith. But the gift must be be received and lived intensely. He proclaims having received salvation but also says that salvation is ongoing. Therefore, salvation is the goal of his life. This is why he runs the race with his eyes fixed on the Lord. "I press on toward the goal to win the prize for which God has called me heavenward in Christ Jesus." Philippians 3:14.
There is an ongoing debate on whether many will be saved. Vatican II confirmed that God wants all to be saved (Universal salvific will of God). The Lord is so committed to our salvation that He died on the Cross for us sinners. We have thus the assurance that He wants to pour His mercy upon even the greatest sinners and bring them home to heaven. That is the story of the prodigal son. We are not assured that all will receive the gift or forgiveness and mercy. Some may obstinately refuse it and be lost.
What about those who do not know Christ? Salvation is possible even through an implicit faith in Christ and an implicit desire to enter the Church. Such faith and desire grow from a person's response to God's truth placed in his heart. Ralph Martin's book, Will Many Be Saved? (2012), studies Vatican II's dogmatic constitution, Lumen Gentium 16. The first part treats the possibility of salvation, even for those who, through no fault of their own, have been unable to respond to the Gospel, including those who, through no fault of their own, have not yet come to a basic knowledge of God.
But the plan of salvation also includes those who acknowledge the Creator as the one and merciful God, who on the last day will judge mankind and all things, and as Our Savior wills that all men be saved. Those also can attain to salvation who, through no fault of their own, do not know the Gospel of Christ or his Church, yet sincerely seek God and moved by grace strive by their deeds to do his will as it is known to them through the dictates of conscience. Nor does divine Providence deny the helps necessary for salvation to those who, without blame on their part, have not yet arrived at an explicit knowledge of God and with his grace strive to live a good life.
Many faithful ask why evangelize if many are saved without any knowledge of Christ or his Church? There are several reasons. The first is that love demands it. If we truly know the love of Christ and how He loves all, then we want all to know and love Him. In addition, the Church teaching makes it clear that the risk of hell is real. Lumen Gentium confirms that individuals are responsible, in as much as they can, to receive the Word of God and allow its power to give them a new life in Christ.
Only God can judge, only God knows when there is damnable guilt due to rejection of truth and when individuals are not capable of seeing the truth. However all Christians have a solemn duty given by Christ to evangelize. Christ expects us to collaborate with Him fully in the salvation of our brethren. The following sentences from Lumen Gentium 16 must also be taken into account:
... But often men, deceived by the evil one, have become vain in their reasonings and have exchanged the truth of God for a lie, serving the creature rather than the Creator (cf. Rom. 1:21,25). Or some there are who, living and dying in this world without God, are exposed to final despair. Wherefore to promote the glory of God and procure the salvation of all of these, and mindful of the command of the Lord, "Preach the Gospel to every creature," (Mk. 16:16) the Church fosters the missions with care and attention.
It is possible for men to be saved by following the guidance of the Spirit speaking to their conscience, even without having heard the Gospel. It is also true that the Lord wants all to come to know Him and follow Him and we would be failing the Lord if we do not evangelize. The Council teaches that the Church has a missionary character. The popes after the Council have insisted in the urgency and necessity of evangelization. Pope Paul VI wrote Evangelii Nuntiandi; John Paul II wrote the encyclical Redemptoris Missio, on the missionary character of the Church; Benedict XVI has often written about the need for a new evangelization and has made evangelization the theme of the year of faith.
If impells us to be one with Jesus in His desire to save as many as we can. With Venerable Conchita, we cry: Jesus Savior of men, save them! That is the way of all the saints because love moves the heart to satisfy the beloved. We suffer with Christ for each soul that is in danger of hell. As one with Him we gladly embrace the cross for their salvation and our own. That is why St. Paul said "Yet when I preach the gospel, I cannot boast, for I am compelled to preach. Woe to me if I do not preach the gospel!" -1 Corinthians 9:16