For me, #1 comes from Pope St. Pius X's Vacantis Apostolicae Sedis. By that I mean specifically, that the pope telling us how we identify the next pope is all I need for certainty. That the pope actually said this, is dogmatically certain - is it not?
In a nutshell, the whole notion of even needing "dogmatic proof" revolves around people not believing what they see, namely, popes publicly sinning and promoting sin. They see the sin, they know it's a sin, but they see the pope and don't believe he's a pope because they've been led to believe that a pope cannot sin, or at least sin *like that*. Where is that dogma by the way? But when one accepts that he is the pope and that he can sin *like that*, then that whole particular problem is solved for them.
It’s not just that. It’s that you basically don’t believe it’s possible to obey him... at all. You can’t even attend a mass that he approves, even a Latin Mass, because that would be a compromise of some sort. There is at the least a real tension there beyond just “popes sin grievously”
And to be clear, I’m technically closer to your side of the debate.