Everyone is familiar with Luther’s heretical teaching known as salvation through faith alone. This means that the single act which is necessary for salvation is faith, which for him, and for protestants in general, means trust in God. For Catholics faith means the assent of the intellect, by means of a supernatural virtue infused by God, to the truths revealed by God and proposed as such by the teaching authority of the Roman Catholic Church. Therefore for Luther, and for those who follow him, sins do not count against you in the order of salvation. There is no need to mortify yourself. No need to do penance. Luther said: “Be a sinner and sin boldly, but believe and rejoice in Christ even more boldly…No sin will separate us from the Lamb, even though we commit fornication and murder a thousand times a day” 
No Catholic would ever hold this. Every Catholic knows that he will be judged on his actions when he dies, and not merely on his trust in God. Nonetheless there are many Catholics, and I am referring to those who have rejected Vatican II and adhere to the traditional Faith, who hold an equivalent formula, which I describe as salvation by piety alone.
This is the typical case. Such a Catholic believes all that the Church teaches, recites faithfully his Rosary frequently, even every day, goes to Mass every Sunday, goes perhaps to devotions during the week, goes to confession often, and has many pictures of Our Lord, Our Lady, and the saints in his house. He may even conduct the family rosary every night in his home.
On the other hand, this same Catholic will live by all of the standards of the modern culture. He watches impure movies on television, the theater, or the internet. He listens to rock music. He raises his children according to all of the modern ideas, that is, permitting them to follow their instincts without discipline, or by inefficacious discipline. If he is a man, he fails to assert his authority in the home. If she is a woman, she is heavily influenced by feminism, and fails to understand her role in the home.
All of the modern style of clothing is worn, no matter how immodest. They go to crowded beaches where there is grave immodesty. They go to places like Disneyland, which needs no comment.
They accept into their families those who are divorced and remarried, or who are living in fornicatory concubinage.
They send their children off to colleges and universities which are designed to destroy the Catholic Faith in their children as well as their morals. They applaud their achievement when they graduate, thinking nothing of the spiritual destruction of the child.
They approve of spouses for their children who are heretical, godless, and/or impure.
And when finally all is said and done, and their children are grown and have become atheists and leftists, these same Catholics will come to the priest and ask, “Where did I go wrong?”
They went wrong in the same way that Luther went wrong. They thought that piety alone would make their children Catholic, and would protect them from bad influences of the modern world. For Luther it was faith alone; for these Catholics it is piety alone.
Contemplate the Holy Cross. There are two great lessons in the Cross of Christ: (1) the love of Jesus for His Father; (2) the putting to death of the old Adam of sin.
Our Lord on the Cross obtained our salvation by giving His Father, in the name of the humanity which He had Himself taken, the obedience to His will, even to the death on the Cross.
This obedience of Christ was the remedy for the disobedience of Adam, and ultimately of every human being who commits a sin. The fragrance of His Son’s obedience far outweighed the stench of human sin. This is one aspect of the redemption of the human race.
The other aspect is the mortification of the man of sin. There was a death penalty to be paid for the sins of men, and Our Lord paid it. Catholic spiritual life is based on these two aspects of the Cross. On the one hand there is love of God, which includes obedience to the commandments of God and piety, that is, all of the acts of adoration and prayer which we offer to God. On the other hand, there is mortification, that is, the putting to death in our souls of the effects of sin, original sin and actual sin. Part of this mortification is the avoidance of the occasions of sin.
The modern culture is a product of the devil, and is one, enormous occasion of sin. Piety will not be pleasing to God, and will produce no good effect, if Catholics are imbibing every day the poisoned cup of the modern culture.
If Catholic parents want to raise Catholic children and not pagan children, and if they want Catholic grandchildren, it is necessary that they cut from the modern world. It requires a great deal of sacrifice. They cannot frequent or enjoy many things which others frequent and enjoy. Children must understand the necessity of this mortification and sacrifice.
I am sure that the Catholics who lived in the Roman Empire in the early days of the Church had the same problem. Rome was a place of wanton debauchery, cruel games, gross immodesty, idolatry, and superstition. The Church flourished, however, in these early times, and it is because the Catholics kept themselves away from the pagan culture of their time.
 Weimar ed. vol. 2, p. 372; Letters I, Luther’s Works, American ed., vol. 48, p. 282.