Actually, the principle is the opposite, "a doubtful pope is no pope". Look it up (papa dubius papa nullus)
AH, the principle of doubt is not purely negative, but positive probable doubt.
Now, undoubtedly he has said and done things that are at least apparently contrary to the faith, but on the other hand he alternates these acts with Orthodox statements, for example that Christ cannot be properly worshipped or sought outside of the Church.
This kind of alternation is indicative of many plausible scenarios. Is the Pope mentally unstable? Is he possessed? Is he being drugged? Or are his notions of the faith not so much formally heretical as much as just badly formed?
And before you tell me even a material heretic cannot be a Pope and refer to Pope Pius XII, you have to understand the context of the term "Material Heretic."
A material heretic is not a person who pronounces heretical words, a material heretic is a person who finds themselves outside the communion of the Catholic Church and, through no fault of their own, finds themselves believing matter that has been objectively condemned as heresy.
In this sense a material heretic cannot be Pope, as in a person who is in good faith but outside the Church's communion is outside the pale as a Papal candidate.
Now, Francis is not a material heretic. He is a Catholic whose actions are proximate to heresy and are pending canonical correction and review.
Those fine distinctions and such... ;-)
Now, there is no positive probable doubt regarding his election, there is no positive probable doubt regarding his enthronement and there is no positive probable doubt regarding the submission of Cardinals nor his acceptance as Pope by the laity.
Therefore in the mind of the Church, which infallibly ascertains matters of dogmatic fact, he is Pope. YOUR job is to submit to the Church's recognition of that and accept that he, as Pope, has done what he has done.