The LDS propose that the Catholic Church went completely apostate very early on. LDS point to certain NT passages that appear to show that the Great Apostasy was in progress even during the Apostolic Age. In fact, there is no question, utterly none, that many people apostasized from the Catholic Faith during and after the Apostolic Age, and have done so throughout history.
One reason, say the LDS, is persecution. They say that persecutions implemented against Christians by governments and plain folk were instrumental in causing the apostasy.
However, by the same measure, the LDS are also apostate. Many early LDS personages apostasized. In fact, most of Joseph Smith’s best friends and associates fell away. For instance the very first members of the First Presidency, Jesse Gause and Sidney Rigdon both fell away. Gause went on a mission a few months after being elevated to the high office, and never came back. Rigdon, chosen as Joseph’s running mate in the 1844 Presidential election, is one of Mormonism’s most famous apostates. There are many others. In fact, the Mormon religion fell apart after Smith’s murder, with several factions going separate ways, such as what became known as the RLDS.
As far as persecution goes, by the LDS own story-telling, there was no shortage of persecution of the LDS people during their early years. The LDS claim (against all historical evidence to the contrary) that persecution helped kill the Catholic Church, but somehow had an opposite effect upon the Mormons.
So, there were apostates in the Catholic Church from the very beginning. But not all went apostate. Not even very many, and certainly none of the Apostles, except Judas Iscariot. Nevertheless, the Mormons claim that so many went apostate that the very authority of the Catholic Church was removed from the Earth by God. Meantime, the LDS had almost ALL of its highest leaders go apostate, going so far as to oppose Joseph Smith publically and incite his killing in June 1844, followed by the disintegration of the LDS church into several factions, and yet THEY aren’t apostate.