My friend, the Pope is not even a member of the Orthodox Christian faith

I think you're thinking of Eastern Orthodox Christianity, where I meant little o orthodox. He's also head of the big and little c catholic church, which, again, gives him authority to define it as he wishes. You don't have to agree with it, and that's fine.

They should rename the fallacy "no true Christian" at this point as 99.9% of times I see that fallacy, it's in this context.

It certainly would be more relatable to more people. Again, I disagree that it applies in this case. It isn't some random person saying these people aren't Christian. It's the person in charge of Christianity (at least, his flavor of it, by catholic implies all of them). The reason there are so many forms of Christianity is because people won't always agree. That still doesn't make this fallacious though.