The Mystical Body of Christ is the Body of the faithful. The faithful are His members who constitute the Church. The faithful are those who have been baptized with water and profess the true faith, and have not separated themselves from the Church.
The Mystical Body of Christ, the Church
Pope Pius XII - 1943 https://www.papalencyclicals.net/pius12/p12mysti.htm
11. After pondering all this long and seriously before God We consider it part of Our pastoral duty to explain to the entire flock of Christ through this Encyclical Letter the doctrine of the Mystical Body of Christ and of the union in this Body of the faithful with the divine Redeemer;
22. 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.
(. . .) it was on the tree of the Cross, finally, that He entered into possession of His Church, that is, of all the members of His Mystical Body; for they would not have been united to this Mystical Body through the waters of Baptism except by the salutary virtue of the Cross, by which they had been already brought under the complete sway of Christ.
(. . .)
The Samaritans were right in proclaiming Him “Savior of the world”; for indeed He most certainly is to be called the “Savior of all men,” even though we must add with Paul: “especially of the faithful, since, before all others, He has purchased with His Blood His members who constitute the Church.
Summo Iugiter Studio
On Mixed Marriages
Pope Gregory XVI - 1832 https://www.papalencyclicals.net/greg16/g16summo.htm
History of Dictum Against Mixed Marriages
5. Next let Us start with the things which concern the faith which, as We mentioned above, some are endangering in order to introduce greater freedom for mixed marriages. You know how zealously Our predecessors taught that very article of faith which these dare to deny, namely the necessity of the Catholic faith and of unity for salvation. The words of that celebrated disciple of the apostles, martyred St. Ignatius, in his letter to the Philadelphians are relevant to this matter: “Be not deceived, my brother; if anyone follows a schismatic, he will not attain the inheritance of the kingdom of God.” Moreover, St. Augustine and the other African bishops who met in the Council of Cirta in the year 412 explained the same thing at greater length: “Whoever has separated himself from the Catholic Church, no matter how laudably he lives, will not have eternal life, but has earned the anger of God because of this one crime: that he abandoned his union with Christ.” Omitting other appropriate passages which are almost numberless in the writings of the Fathers, We shall praise St. Gregory the Great who expressly testifies that this indeed is the teaching of the Catholic Church. He says: “The holy universal Church teaches that it is not possible to worship God truly except in her and asserts that all who are outside of her will not be saved.” Official acts of the Church proclaim the same dogma. Thus, in the decree on faith which Innocent III published with the synod of Lateran IV, these things are written: “There is one universal Church of all the faithful outside of which no one is saved.” Finally the same dogma is also expressly mentioned in the profession of faith proposed by the Apostolic See, not only that which all Latin churches use, but also that which the Greek Orthodox Church uses and that which other Eastern Catholics use. We did not mention these selected testimonies because We thought you were ignorant of that article of faith and in need of Our instruction. Far be it from Us to have such an absurd and insulting suspicion about you. But We are so concerned about this serious and well known dogma, which has been attacked with such remarkable audacity, that We could not restrain Our pen from reinforcing this truth with many testimonies.
2 Corinthians 4:3-4
And if our gospel be also hid, it is hid to them that are lost, In whom the god of this world hath blinded the minds of unbelievers, that the light of the gospel of the glory of Christ, who is the image of God, should not shine unto them.