“God’s mercy is infinite”
Of course God’s mercy is infinite. God is infinite and therefore His attributes, like His mercy, have to be infinite as well. However, there is a little caveat: His mercy is not infinite towards each individual person. Each person’s earthly life is a time of grace. If he dies rejecting God, the mercy is over for him.
“Everyone is welcome” or “God’s love is unconditional”
Antipope Bergoglio called out during his visit to Lisbon in 2023 to the crowd multiple times: “¡Todos, todos, todos!” (“Everyone, everyone, everyone!”) He told his audience in one of his speeches: “In the Church, no one is left out or left over. There is room for everyone. Just the way we are. […] The Lord does not point a finger, but opens his arms. It is odd: the Lord does not know how to do this (pointing), but that (opening wide). He embraces us all.”
Of course everyone can enter the Catholic Church. However, God has expectations.
“If you would enter life, keep the commandments.” (Mt 19:17)
“Not every one who says to me, ‘Lord, Lord,’ shall enter the kingdom of heaven, but he who does the will of my Father who is in heaven.” (Mt 7:21)
“What does it profit, my brethren, if a man says he has faith but has not works? Can his faith save him? […] So faith by itself, if it has no works, is dead.” (Jas 2:14.17)
God expects us to follow Him, obey His commandments and the legitimate authorities He instituted: the apostles and their successors. Everyone is welcome into the Church, as long as he lets actions follow his words.
“Everyone has equal dignity”
Even before the infamous and blasphemous “Dicastery for the Doctrine of the Faith” letter “Dignitas Infinita” (2024) claimed that “[e]very human person possesses an infinite dignity, inalienably grounded in his or her very being, which prevails in and beyond every circumstance, state, or situation the person may ever encounter”, it was often said that everyone has the same dignity. Let’s see what we can find in Catholic tradition.
The Catholic Church has always believed that Baptism raises the dignity of the recipient. St. Paul explains in his Letter to the Romans:
“We were buried therefore with him by baptism into death, so that as Christ was raised from the dead by the glory of the Father, we too might walk in newness of life.” (Rom 6:4) “For all who are led by the Spirit of God are sons of God. For you did not receive the spirit of slavery to fall back into fear, but you have received the spirit of sonship. When we cry, ‘Abba! Father!’” (Rom 8:14-15)
Through Baptism, the recipient goes from being a slave to sin to being a child of God.
Another example: Pius XII wrote in his encyclical Mediator Dei in 1947:
“88. Nor is it to be wondered at, that the faithful should be raised to this dignity [to participate in the eucharistic sacrifice]. By the waters of baptism, as by common right, Christians are made members of the Mystical Body of Christ the Priest, and by the “character” which is imprinted on their souls, they are appointed to give worship to God.”
“104. Let the faithful, therefore, consider to what a high dignity they are raised by the sacrament of baptism.”
People can also diminish their own dignity by committing sins and can raise their dignity by repentance. Saint Thomas Aquinas explains in his Summa Theologiae:
“By sin, man loses a twofold dignity, one in respect of God, the other in respect of the Church. In respect of God he again loses a twofold dignity. One is his principal dignity, whereby he was counted among the children of God, and this he recovers by Penance, which is signified (Lk. 15) in the prodigal son, for when he repented, his father commanded that the first garment should be restored to him, together with a ring and shoes. The other is his secondary dignity, viz. innocence, of which, as we read in the same chapter, the elder son boasted saying (Lk. 15:29): “Behold, for so many years do I serve thee, and I have never transgressed thy commandments”: and this dignity the penitent cannot recover.” (Summa Theologiae III 89, article 3)
That is, one can recover the dignity of being a child of God, but one cannot recover the innocence.

On the Mount of Olives in East Jerusalem by Stephanie Matthiesen in 2018 under the CC-BY-NC-ND 2.0 license, here