His "out" of using the "formal" vs. "material" heresy distinction is contrary to Bellarmine himself, who writes of MANIFEST heresy.
St. Robert Bellarmine, De Romano Pontifice, Book II, Chap. 30: "… for men are not bound, or able to read hearts; but when they see that someone is a heretic by his external works, they judge him to be a heretic pure and simple, and condemn him as a heretic."
Now, there has to be pertinacity, but who can doubt Bergoglio's pertinacity? Many Catholics have called him out for his heresies, and it's quite clear in the external forum that he pertinaciously adheres to them.
There's been a false theological trend going back a couple hundred years to conflate "formal" heresy with sincerity, something that can only be judged ultimately in the internal forum, which is why St. Robert speaks of judging men heretics by external works (in the external forum) rather than through "read[ing] hearts" (internal forum).
"Formal" heresy refers to where someone implicitly rejects the entire formal motive of faith, i.e. the teaching authority of the Church, rather than being in simple error, typically through ignorance ... and not to sincerity. What heretic didn't "sincerely" believe the heresies he was promoting?