There were some early examples of bishops criticizing the church at Rome, which typically is considered by some as "the church". Saint Polycarp disagreed with Rome over its observance of Pascha (or Easter). This in turn led to Saint Polycratus' disagreement with Pope Victor circa CE 190. Saint Firmilian and Saint Cyprian disagreed with Rome over its observance of baptism.
The following is from Eusebius' recording of the criticism.
- But the bishops of Asia, led by Polycrates, decided to hold to the old custom handed down to them. He himself, in a letter which he addressed to Victor and the church of Rome, set forth in the following words the tradition which had come down to him:
- “We observe the exact day; neither adding, nor taking away. For in Asia also great lights have fallen asleep, which shall rise again on the day of the Lord’s coming, when he shall come with glory from heaven, and shall seek out all the saints. Among these are Philip, one of the twelve apostles, who fell asleep in Hierapolis; and his two aged virgin daughters, and another daughter, who lived in the Holy Spirit and now rests at Ephesus; and, moreover, John, who was both a witness and a teacher, who reclined upon the bosom of the Lord, and, being a priest, wore the sacerdotal plate.
- He fell asleep at Ephesus.
- And Polycarp in Smyrna, who was a bishop and martyr; and Thraseas, bishop and martyr from Eumenia, who fell asleep in Smyrna.
- Why need I mention the bishop and martyr Sagaris who fell asleep in Laodicea, or the blessed Papirius, or Melito, the Eunuch who lived altogether in the Holy Spirit, and who lies in Sardis, awaiting the episcopate from heaven, when he shall rise from the dead?
- All these observed the fourteenth day of the passover according to the Gospel, deviating in no respect, but following the rule of faith. And I also, Polycrates, the least of you all, do according to the tradition of my relatives, some of whom I have closely followed. For seven of my relatives were bishops; and I am the eighth. And my relatives always observed the day when the people put away the leaven.
- I, therefore, brethren, who have lived sixty-five years in the Lord, and have met with the brethren throughout the world, and have gone through every Holy Scripture, am not affrighted by terrifying words. For those greater than I have said ‘We ought to obey God rather than man.’”
- He then writes of all the bishops who were present with him and thought as he did. His words are as follows:
“I could mention the bishops who were present, whom I summoned at your desire;1705 whose names, should I write them, would constitute a great multitude. And they, beholding my littleness, gave their consent to the letter, knowing that I did not bear my gray hairs in vain, but had always governed my life by the Lord Jesus.”
- Thereupon Victor, who presided over the church at Rome, immediately attempted to cut off from the common unity the parishes of all Asia, with the churches that agreed with them, as heterodox; and he wrote letters and declared all the brethren there wholly excommunicate.
Polycrates is basically criticizing Victor of Rome for not following apostolic teaching.
This next example is a letter from Firmilian to Cyprian criticizing Pope Stephen's allowance of heretical baptism as equal to Christian baptism. In his letter, he references the aforementioned Easter controversy, saying Rome feigns apostolic authority.
- But, moreover, you have well answered that part where Stephen said in his letter that heretics themselves also are of one mind in respect of baptism; and that they do not baptize such as come to them from one another, but only communicate with them; as if we also ought to do this. In which place, although you have already proved that it is sufficiently ridiculous for any one to follow those that are in error, yet we add this moreover, over and above, that it is not wonderful for heretics to act thus, who, although in some lesser matters they differ, yet in that which is greatest they hold one and the same agreement to blaspheme the Creator, figuring for themselves certain dreams and phantasms of an unknown God. Assuredly it is but natural that these should agree in having a baptism which is unreal, in the same way as they agree in repudiating the truth of the divinity. Of whom, since it is tedious to reply to their several statements, either wicked or foolish, it is sufficient shortly to say in sum, that they who do not hold the true Lord the Father cannot hold the truth either of the Son or of the Holy Spirit; according to which also they who are called Cataphrygians, and endeavour to claim to themselves new prophecies, can have neither the Father, nor the Son, nor the Holy Spirit, of whom, if we ask what Christ they announce, they will reply that they preach Him who sent the Spirit that speaks by Montanus and Prisca.
They continue in their criticism.
- And as Stephen and those who agree with him contend that putting away of sins and second birth may result from the baptism of heretics, among whom they themselves confess that the Holy Spirit is not; let them consider and understand that spiritual birth cannot be without the Spirit; in conformity with which also the blessed Apostle Paul baptized anew with a spiritual baptism those who had already been baptized by John before the Holy Spirit had been sent by the Lord, and so laid hands on them that they might receive the Holy Ghost. But what kind of a thing is it, that when we see that Paul, after John’s baptism, baptized his disciples again, we are hesitating to baptize those who come to the Church from heresy after their unhallowed and profane dipping. Unless, perchance, Paul was inferior to the bishops of these times, so that these indeed can by imposition of hands alone give the Holy Spirit to those heretics who come (to the Church), while Paul was not fitted to give the Holy Spirit by imposition of hands to those who had been baptized by John, unless he had first baptized them also with the baptism of the Church.
His letter is a very interesting read, especially given that the Catholic Church finally recognizes in LDS baptism the same problem that Stephen failed to grasp.
So yes to the OP, there have been saints who have criticized what is known as the Catholic Church.