Comparing earthly marriage between man and woman to Christ’s love for His Church, St. Paul teaches:
Christ loved the church and gave himself up for her to make her holy, cleansing her by the washing with water through the word, and to present her to himself as a radiant church, without stain or wrinkle or any other blemish, but holy and blameless. (Ephesians 5 25-27)
So, if the Church is who she claims to be, the Bride of Christ, then, no, she can not sin. She has been made, by Christ Himself, to be “without stain or wrinkle or any other blemish, but holy and blameless.”
For instance, if it was 1955 and my Parish told me it was OK to eat meat on Friday - would that be the “church” sinning? This example is hypothetical but what if it happened. Would it again just be the “priest” who said it be sinning?
I don’t know much about your experience with the Catholic Church or various “Parishes,” but generally speaking a Catholic parish does not “tell” people things in the way you are asserting. Priests do. Deacons do. Catechists do, etc. These teachers and leaders can and often do speak in concert, but they are responsible as individuals for their teaching among the flock (see 2 Peter 2).
I’m not entirely sure I understand your question, though. Are you asking: if a particular parish, or group of people, followed the “it’s okay to eat meat on Friday” teaching of a priest, would each individual be culpable for that disobedience or is only the priest culpable?
If this is your question and I have understood it correctly, the answer is: it depends.
I imagine it is POSSIBLE, within a large parish, that there are those people who, through no fault of their own, could possibly be ignorant of certain universal teachings. One example would be a child, within the age of resposibility for observing fasts and abstinances, who has never been taught correctly nor who has the means or maturity to seek proper instruction. This person could be completely inculpable for the objective disobedience of not observing the Friday ordinances.
However, I think this measure of innocence is quite rare. Often times, people, fully knowing or at least with some idea of the universal teachings of the Church, actually seek affirmation for disobediences they intend to commit. And, as Scripture clearly warns, there are swarms of false teachers who would readily mislead the flock for their own purposes. Some do so neglectfully, as St. Paul warns: **When you sin against your brothers in this way and wound their weak conscience, you sin against Christ. Therefore, if what I eat causes my brother to fall into sin, I will never eat meat again, so that I will not cause him to fall.(1 Corinthians 8:12-13)**Some do so for their own purposes, causing others to be tossed back and forth by the waves, and blown here and there by every wind of teaching and by the cunning and craftiness of men in their deceitful scheming. (Ephesians 4:14)
But, in any case, if a teacher knowingly causes someone to stumble, they will be held responsible for their teachings, for as the author of the letter to the Hebrews writes: Obey your leaders and submit to their authority. They keep watch over you as men who must give an account. (Hebrews 13:17)
Now, if a particular priest actually commanded his parish flock to disobey a universal church teaching, one would think that the full weight of his treachery would fall upon him. But, this is such an unlikely predicament especially with the relatively quick reporting and response to disobediences and the wide accessibility to truth we have in this modern world.
With today’s climate of information technology, it is quite unlikely that someone could grow up Catholic, with proper catechesis, and have no clue what the Church really teaches or at least how to find it out. Thus, even with a wayward nod from a priest, a person disobeying a teaching from which she is seeking an excuse would be responsible for her own sin of disobedience. For, as St. Paul also teaches: So then, each of us will give an account of himself to God. (Romans 14:12)