The Roman Catholic Church has survived bad Popes in the past and will survive Francis.
A well formed Catholic knows that the Pope can not change doctrine.
I fear for the RCC in the counter-reformation era. The bad popes in the past occurred when the RCC was more conciliatory (in the past the popes who tried to flex too much authority had it reigned in at the next Council). The Jesuits are a relatively new order (about 4 centuries old) within the RCC that was formed shortly before the Council of Trent and, IMHO, was given much power in the teachings of the RCC because they were all about papal supremacy (countering the Protestants criticisms of the pope). Thus, unlike the RCC in the past, the RCC as we know it for the past 4 centuries is too used to the pope being the see-all, do-all above all criticism.
Will this be enough to shake up the RCC and bring things back more to right? Or are we entering yet another era where yet another heresy is going to be taught as "truth" "tradition" as though it's always been? For example, what we call "traditional Latin mass" isn't some 2,000 year old tradition like they make it out to be. It was codified at the Council of Trent in the 16th century (again, trying really hard to be different from Protestants). Can you find early Catholic catechisms written before the Protestant Reformation that mentions the pope? These are examples of teachings that Catholics before then would have never thought would have been taught for centuries as truth like Catholics today hear it.
So will future Catholics quote the glories of gay hedonism as though it's always been part of "truth" "tradition"? Or will this be the moment that Catholics tell the pope and his supporting clergy that truth comes from the Bible and anything they teach will be tested by that? (see tagline)