Typically wry British remarks from a very orthodox Catholic priest and classicist, of the Anglican Ordinariate:
To this question there can only be one answer: NO. And NO means…NO.
Pope Bergoglio has NEVER, to my knowledge, formally enunciated doctrines which are unambiguously heretical. The claim one sometimes hears, to the effect that he has formally, as if from his chair, made doctrinal assertions which the Church has formally defined as heretical, is NONSENSE…
One easy reason for being confident that the Sovereign Pontiff has not formally taught heresy is the simple fact, confirmed pretty well every time he opens his mouth, that he despises theology and holds doctrine in not-even-barely-concealed contempt.
To be a heretic, or, more precisely, to be a formal heretic, it is in practical terms necessary to operate within the respectable constraints of propositional discourse. The fact that Bergoglio does not do this is proved by the fact, written large over this whole pontificate, that nobody ever quite seems to be sure what he means.
The DUBIA which the four Cardinals put forward provide a good example of this. Four men of erudition (not to mention seniority) thought they needed to ask the Bishop of Rome what he meant. His tardiness, so far, in exercising the Petrine Ministry of Confirming his Brethren demonstrates his resolute determination not to be tied down by propositions.
I do not believe that it is possible to convict such a man, operating such a policy, of being a formal heretic. Those who wish to do this are walking up quite the wrong garden path. And I will argue that they are guilty of a genre-error.
Source: Fr Hunwicke’s Mutual Enrichment