A reader asked me this question this weekend, and I shall try and answer this.
First of all, the laity are "in" the world. That is, we work, eat, sleep, study, do whatever in the context of the City of Man. We are called to build up society through our good works and virtues. Of course, as Catholics, we know that there is no separation between Church and State, which means that the Church has the duty and right to inform the State as to morals and ethics.
Natural law bind the Church with the good of the commonweal. And, it is the duty of the State to protect the Church. But, of course, this is not happening. Most states are openly at odds with the Catholic Church, as most states now are build on modernist "isms" which degrade the dignity of the individual and undermine the soul as well as the body of the person.
Personhood is under attack world-wide. The Catholic finds himself in the position of believing and acting contrary to many unlawful laws, such as abortion, same sex marriage and euthanasia, all sins against both natural law and revealed law.
The person in the world tries to work in an increasingly hostile environment of sin and corruption. To be in the world is painful and conflict will naturally arise. The lay person is to change the evils of the world, not compromise or give in to such evils.
To be in the world means to be on the front lines of the Church Militant. We are not yet the Church Triumphant, those in heaven, nor are we the Church Suffering, those in purgatory, but the soldiers on the ground. To use this military language is in keeping with the Scriptures themselves. Here is Ephesians 6.
10 Finally, brethren, be strengthened in the Lord, and in the might of his power.
11 Put you on the armour of God, that you may be able to stand against the deceits of the devil.
12 For our wrestling is not against flesh and blood; but against principalities and power, against the rulers of the world of this darkness, against the spirits of wickedness in the high places.
13 Therefore take unto you the armour of God, that you may be able to resist in the evil day, and to stand in all things perfect.
14 Stand therefore, having your loins girt about with truth, and having on the breastplate of justice,
15 And your feet shod with the preparation of the gospel of peace:
16 In all things taking the shield of faith, wherewith you may be able to extinguish all the fiery darts of the most wicked one.
17 And take unto you the helmet of salvation, and the sword of the Spirit (which is the word of God).
18 By all prayer and supplication praying at all times in the spirit; and in the same watching with all instance and supplication for all the saints:
It is clear that to be in the world is basically a daily fight, an entering into a battleground where those who hate God and the Church fight against us.
We are in this battle because of our baptism.
Now, to be not of the world means that we do not conform to the mind of the world, but the Mind of Christ. We see things differently than those who are of the world as well as in it. And, it is our duty to conform our minds to that of Christ, which we learn about in and through the Church.
Notice that St. Paul states clearly that we have the Mind of Christ. How so? Through the adoption as sons and daughters of God through baptism, through sanctifying grace given in the sacraments, and through the life of the virtues and subsequent gifts of the Holy Spirit.
1 Corinthians 2:16
16 For who hath known the mind of the Lord, that we may instruct him? But we have the mind of Christ.
What an astounding statement-we already have the Mind of Christ is we are in the Church in sanctifying grace. This is what it means to be "not of the world", as Christ is not of the world. We see and judge things from His perspective, and grow in objectivity, which is real maturity. (Those who remain stuck in subjectivity are both spiritual and psychologically immature.)
To be not of the world means we can step back and see the errors, the sins in the City of Man and try to build the City of God. Building up the Kingdom of God means allowing God to purify us first, like good soldiers trained for war.
If we conform to the world, we lose our perspective and our consciences suffer a great loss of discernment.
The trouble with most Catholics is that they have compromised so much they have lost this keen sight to discern good and evil.
One can gain this objectivity again through repentance and absolution in the sacrament of confession.
The more one conforms to the world either in standards or in interests, the more one loses the cutting edge of thinking with the Mind of Christ.
The more one conforms to the teachings of the Church and the more one allows the Holy Spirit to show one the evils of things in the world, such as certain types of movies, music, entertainments of other sorts, television programs, books, magazines, and even friends who indulge in the world, the more one will be not of the world, although in it.
Again, too many people have fallen into the carelessness of conformity.
Yesterday, in the Gospel for the Feast of the Presentation, Christ was addressed as the "sign of contradiction" in the world.
Always, that is what we are called to be. Blessed John Paul II in his 1979 book Sign of Contradiction noted that this is the definition of the Church in the world.
All of us are called to holiness. All are called to perfection. Like Christ, Who was in the world but not of the world, we are called to manifest God.
May I add that as the world becomes more immersed in evil, we shall be even less of the world. This will become an inevitable reality as people choose darkness over the light. For the sake of our own souls, we shall have to distance ourselves from things which we could be free to partake in within living memory.
But, to compromise is to endanger our own salvation.
I hope this, at least partially, addresses the question from a reader.