Considering you have Catholics questioning, rightly, his actions, I’d say stability is already a problem.
None of those questionable things involve matters of Catholic dogma. So stability of the Church as a social group may indeed be elusive, but it is not at all a new phenomenon. We’ve seen worse: the Western Schism, iconoclasm, entire monastic orders suppressed, Catholic splinter groups forming left and right. The stability of the Church as a supernatural body of the faithful on earth and in heaven, however, cannot be threatened by this, and is not. The pope’s still Catholic.