Do the religious differences between europeans resemble the arguments between different groups of believers in the other major world religions?

He Protestant Reformation challenged Apostolic Succession, meaning that Jesus appointed Peter, who appointed leaders who have an unbroken chain. With Luther viewing the Church as abusing its power, he challenged this unbroken chain. This also lead to other beliefs, such as questioning papal infallibility. Easily seen in Shi'a or Sunni beliefs. Shia believing the 12 infallibles, while Sunnis declining that they are infallible. 

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