Let's go back to this interesting notion of Anglo-Papalism or Anglican Papalism, which I take to be synonymous usages on either side of the Atlantic. If I were an inquisitor, which is what people in the CDF used to be, I would want to interrogate self-identified Anglican Papalists on exactly what they believed, but failing that opportunity, I will propose that they claim in some way to be both Anglican and Catholic, in particular from the Papalist side acknowledging the authority of the Pope.
But this is contradictory, a lot like the folks who more recently acknowledge that they have chromosomes characteristic of one gender, but identify as the other, or both, or something else. A Catholic who'd been reading St Alphonsus Liguori might reasonably conclude there are issues relating to the sixth commandment in operation here that probably make the protestations less than sincere. What's behind the contradiction in the case of Anglican Papalists?
My visitor has characterized Fr Hunwicke as an Anglo-Papalist, and Msgr Steenson has elsewhere been characterized as an Anglican Papalist, so for convenience, I'll refer to them that way, recognizing they may dispute this themselves.
At basis, we're multiplying entities. An ordinary Catholic is defined as such in the Catechism, but we're creating a secondary category called "Anglican Papalist". Why? This certainly implies that, for example, Fr Hunwicke or Msgr Steenson had some special qualifications for this category beyond my neighbor Vinny, who goes to St Ipsydipsy. Beyond that, my other neighbor, Chadwick, comes from a recusant family in the UK and is not an Anglican Papalist either. And Stanley, behind me, is a high-church Episcopalian who's happy in his parish with Mother Susan as his rector.
So there is some need to multiply the entities, but we're not sure what it is -- I think we're still in the territory of those who advocate for 57 genders. We've multiplied entities largely due to certain private reservations that are never clearly expressed.
We also have the issue of what happened to Anglican Papalists after 2011-12. Did they all go into ordinariates? Did they all automatically become Catholic in any case? Let's take Chichester, a cradle Anglican who later in life identified as an Anglican Papalist. Even given the option of becoming a Catholic in a newly-erected ordinariate, he still would have needed to go through catechesis and receive the sacraments of initiation. Did he? Is he still entitled to call himself an Anglican Papalist if he didn't? Probably. After all, "Anglican Papalist" is never clearly defined anywhere and is always a matter of private judgment, just like which of the 57 genders one might feel like that day.
Let's take the specific problems raised by Fr Hunwicke and Msgr Steenson. At the time they became Catholic via Anglicanorum coetibus, did thy cease to be Anglican Papalists and become simple Catholics? I would say most certainly not. They seem to consider themselves a special new kind of Catholic, judging at least from external impressions. Isn't this a little like the guy who goes through transgender surgery and won't keep quiet and just live as a woman? Instead, he's going onto TV shows to plead his case that he's something special.
Apologists for whatever Anglican Papalists are, precisely, in the post-Anglicanorum coetibus world, are going to insist they bring something special with them, precious treasures of the Anglican spiritual patrimony. In other words, they don't seem to want to shut up and go to confession. They point instead to some vague business that amounts, as a visitor exposed to an OCSP group described it recently, to Tolkien-y hipsterism.
I think there's a great deal of reason not to trust this. I'm not sure why the successors to the Grand Inquisitor ever thought this was a good idea.