Veteran Vatican correspondent John L. Allen speculates on what will happen if the Synod ends with conservative laity believing that the Pope is not on their side. Some will hunker down in their own parishes, if they have good ones, but others may drift away from involvement in Church activities, he says. And this could significantly damage the Church, in his view.
Assuming that conservative (or, as I prefer, orthodox) Catholics find themselves alienated from Francis in the way many liberal Catholics were from Benedict, I think few orthodox Catholics will leave the Church over it. After all, as Allen says, they are tied to the RC institution as liberal Catholics are not. Relatedly, they know as a matter of theological conviction that a bad pope does not invalidate the truths proclaimed by the Church. They will dig in and endure (though this caveat: it is dangerous to believe that doctrinal conviction will be enough to hold all conservative believers; faith is not based on reason alone). Allen would know better than I, certainly, but I do not see an exodus into Orthodoxy or any other form of Christianity.
What Francis risks is these orthodox Catholic believers seceding in place from the institutional church. For example, you find in some places independently-run Catholic schools that exist outside the diocesan bureaucracy. These schools are typically formed by parents dissatisfied with the official Catholic schools, and who want their children to receive a more robust and orthodox Catholic education. Or, these parents homeschool. Some of them make involvement in Catholic groups like Opus Dei the center of their faith activity, and not the parish — this, not because of any sinister reason, but because they want to be spiritually fed, and they’re not getting it at parishes run like sacrament factories.
And so forth. This, I believe, is the sort of danger Francis faces in trying to liberalize the Church: the laypeople most committed to the faith withdrawing from active participation in the Church’s official ministries, and instead pouring their energy and their money into parallel Catholic institutions, with the broad idea being that the faith needs some institutional expression to endure the long dying of the liberalized mainstream within the Catholic Church.
I already see this happening. It was happening before Pope Francis.