Mormons don’t believe in Catholic authority because they are at root radical Protestants who believe the Catholic Church fell into apostasy. Arguing about apostolic succession with Mormons is useless since they start from a 19th century Protestant understanding which rejects Catholicism’s authority completely.
Well, this thread could become interesting…
It’s true that the LDS don’t believe in the authority of the RCC; nor does it believe the claims of any other Church that claims an unbroken succession back to Peter and the other Apostles (as I assume the Orthodox make). But it’s incorrect to state there’s a Protestant root or aspect to it’s founding. LDS routinely hear in Sunday School that if the RCC is true then the Protestant churches must be false because they broke away from the true church, and that if the RCC is false then the Protestant churches must be false since they broke away from a false church. (See Joseph Smith quote further down.) Also, the claim of Joseph Smith is that he was told by Jesus Christ to not join any sect because they were all wrong.
LDS believe we have a Biblical understanding of an apostasy (see Acts 20:29, 2 Thessalonians 2:1-3, Galatians 1:6, 1 John 2:18, 19, 3 John 9, etc.) and subsequent restoration (Acts 3:20, 21)
Regarding apostolic succession, LDS believe that John the Baptist, and later Peter, James, and John appeared to Joseph Smith to restore Priesthood authority on the Earth, which along with the apostasy verses cited earlier are the main reasons that claims of authority by other churches are rejected by the LDS. I’d say a majority of devout LDS are unfamiliar with the term “apostolic succession” as used by orthodox Christianity. The similarities between LDS and Protestants regarding the Catholic Church probably start and stop with the agreement that the RCC didn’t have authority. Did 19th century Protestants believe that authority needed to be restored? Isn’t there a “priesthood of believers” concept in Protestant faiths?
Joseph Smith did say these things about the Catholic Church…
*"The old Catholic church traditions are worth more than all you have said. Here is a principle of logic that most men have no more sense than to adopt. I will illustrate it by an old apple tree. Here jumps off a branch and says, I am the true tree, and you are corrupt. If the whole tree is corrupt, are not its branches corrupt? If the Catholic religion is a false religion, how can any true religion come out of it? If the Catholic church is bad, how can any good thing come out of it? "
“I testify again as God never will acknowledge any apost[ate]: any man who will betray the Catholics will betray you–& if he will betray one anoth[e]r. he will betray you”*
I don’t know the full context of the second quote, except that there probably were very few Catholics near Joseph Smith in his day.
And finally, just because there was an Apostasy in the LDS view doesn’t mean that no one found God. John Taylor (successor to Brigham Young) wrote:
“I have a great many misgivings about the intelligence that men boast so much of in this enlightened day. There were men in those dark ages who could commune with God, and who, by the power of faith, could draw aside the curtain of eternity and gaze upon the invisible world. There were men who could tell the destiny of the human family, and the events which would transpire throughout every subsequent period of time until the final winding-up scene. There were men who could gaze upon the face of God, have the ministering of angels, and unfold the future destinies of the world. If those were dark ages I pray God to give me a little darkness, and deliver me from the light and intelligence that prevail in our day; for as a rational, intelligent, immortal being who has to do with time and eternity, I consider it one of the greatest acquirements for men to become acquainted with their God and with their future destiny.”