From Pope Pius XII’s encyclical Mystici Corporis Christi (1943):

Nor must one imagine that the Body of the Church, just because it bears the name of Christ, is made up during the days of its earthly pilgrimage only of members conspicuous for their holiness, or that it consists only of those whom God has predestined to eternal happiness. It is owing to the Savior’s infinite mercy that place is allowed in His Mystical Body here below for those whom, of old, He did not exclude from the banquet.²⁰ For not every sin, however grave it may be, is such as of its own nature to sever a man from the Body of the Church, as does schism or heresy or apostasy. Men may lose charity and divine grace through sin, thus becoming incapable of supernatural merit, and yet not be deprived of all life if they hold fast to faith and Christian hope, and if, illumined from above, they are spurred on by the interior promptings of the Holy Spirit to salutary fear and are moved to prayer and penance for their sins.

Let every one then abhor sin, which defiles the mystical members of our Redeemer; but if anyone unhappily falls and his obstinacy has not made him unworthy of communion with the faithful, let him be received with great love, and let eager charity see in him a weak member of Jesus Christ. For, as the Bishop of Hippo remarks, it is better “to be cured within the Church’s community than to be cut off from its body as incurable members.”²¹ “As long as a member still forms part of the body there is no reason to despair of its cure; once it has been cut off, it can be neither cured nor healed.”²²

²⁰ Cf. Matth., IX, 11; Mark, II, 16; Luke, XV, 2.
²¹ August., Epist., CLVII, 3, 22: Migne, Patrologiæ Cursus completus, Series Latina [PL], XXXIII, 686.
²² August., Serm., CXXXVII, 1: PL XXXVIII, 754.

— Mystici Corporis Christi 23-24

From Pope Pius XII’s encyclical Mystici Corporis Christi (1943):

For the social needs of the Church Christ has provided in a particular way by the institution of two other Sacraments. Through Matrimony, in which the contracting parties are ministers of grace to each other, provision is made for the external and duly regulated increase of Christian society, and, what is of greater importance, for the correct religious education of the children, without which this Mystical Body would be in grave danger. Through Holy Orders men are set aside and consecrated to God, to offer the Sacrifice of the Eucharistic Victim, to nourish the flock of the faithful with the Bread of Angels and the food of doctrine, to guide them in the way of God’s commandments and counsels and to strengthen them with all other supernatural helps.

In this connection it must be borne in mind that, as God at the beginning of time endowed man’s body with most ample power to subject all creatures to himself, and to increase and multiply and fill the earth, so at the beginning of the Christian era, He supplied the Church with the means necessary to overcome the countless dangers and to fill not only the whole world but the realms of heaven as well.

Actually only those are to be included as members of the Church who have been baptized and profess the true faith, and who have not been so unfortunate as to separate themselves from the unity of the Body, or been excluded by legitimate authority for grave faults committed. “For in one spirit” says the Apostle, “were we all baptized into one Body, whether Jews or Gentiles, whether bond or free.”¹⁷ As therefore in the true Christian community there is only one Body, one Spirit, one Lord, and one Baptism, so there can be only one faith.¹⁸ And therefore, if a man refuse to hear the Church, let him be considered—so the Lord commands—as a heathen and a publican.¹⁹ It follows that those who are divided in faith or government cannot be living in the unity of such a Body, nor can they be living the life of its one Divine Spirit.

¹⁷ I Cor., XII, 13.
¹⁸ Cf. Eph., IV, 5.
¹⁹ Cf. Matth., XVIII, 17.

— Mystici Corporis Christi 20-22