Who are you to decide whether the Pope is a believer or a non-believer? Or the bishops of the SSPX, for that matter?
If he were a believer he would preach the Gospel and not preach modernism.
The Catholic Church is the Church founded by Jesus Christ, with the promise that it would endure until the end of time and that the Gates of Hell would not prevail against her. "Where Peter is, there is the Church" should be enough of a clue for anyone claiming to be Catholic.
The successor to Peter wouldn't do what he has done.
Throughout time, there have been those who seek to usurp God and set up their own churches and religions, and many of them have been highly skilled in half-truths and obfuscations to justify their position.
If they believed in the miracles of scripture they have more Faith than Benedict XVI.
At the end of the day, we have to trust to Scripture and to the Magisterium of the Church.
Which is why a modernist cannot be followed as its head.
Cardinal Ratzinger:
The text [of the docuмent Instruction on the Theologian's Ecclesial Vocation] also presents the various types of bonds that rise from the different degrees of magisterial teaching. It affirms - perhaps for the first time with this clarity -
that there are decisions of the magisterium that cannot be the last word on the matter as such, but are, in a substantial fixation of the problem, above all an expression of pastoral prudence, a kind of provisorial disposition. The nucleus remains valid, but the particulars, which the circuмstances of the times influenced, may need further correction.
In this regard, one may think of the declarations of Popes in the last century [19th century]
about religious liberty, as well as the anti-Modernist decisions at the beginning of this century, above all, the decisions of the Biblical Commission of the time [on evolutionism]. As a cry of alarm in the face of hasty and superficial adaptations, they will remain fully justified. A personage such as Johann Baptist Metz said, for example, that the Church's anti-Modernist decisions render the great service of preserving her from falling into the liberal-bourgeois world. But in the details of the determinations they contain, they became obsolete after having fulfiled their pastoral mission at their proper time.
Neither of which support the position that Mr. J. Smith of Nowheresville has assumed the position of Pope and set up a new Church because he wasn't happy with the way that our Lord's Church was going.
There's no point following a leader who doesn't believe the religion.
If the religion is true, it's better to be in nobody in nowhereville than to follow a veritable apostate.
For sure, there are battles to fight, but those battles ought to be fought from within, rather than from the outside. Remember, nothing will prevail against the Church.
No, not the true Church, but as St. Athanasius said, that could be reduced to a handful.
If you willingly follow an unbeliever who rejects the miracles of scripture ultimately you cannot maintain the Catholic Faith.