At the same time, Anglicanism overall is a moving target. It's pretty unusual in the US to attend an Episcopal eucharist that isn't held in a church with candles on the altar, a reredos, stained glass, and a communion rail, with clergy in Tridentine vestments. Before the late 19th century, many of these would be cause for scandal and, in the UK, even prosecution, but they're now common even in the lowest-church parishes, at least in the US.
We might also say that an Anglo-Papalist believes Anglicans should return to Papal authority, but here, Catholicism is a moving target. Some historians trace the rise of the movement to Apostolicae curae, the 1896 encyclical that declared Anglican orders null and void, but in the US, there are three formal paths for Anglicans to become Catholic, either as priests or laity, as individuals or with groups -- RCIA, the Anglican Use Pastoral Provision, and the US-Canadian Ordinariate.
However, a bishop can ordain a former Anglican outside these structures, as was done with Fr Barker, and a priest can receive lay Anglicans outside the RCIA process. As a practical matter, there are few obstacles to Anglicans becoming Catholic even outside Anglican Use or the Ordinariates, and thousands probably do this each year -- but they're hardly Anglo-Papalists.
So Anglo-Papalism is hard to define without a context. In context, at its peak between 1900 and 1960, it was an extreme, even eccentric, wing of Anglo-Catholicism. Two of its identifying characteristics were use of an unauthorized liturgy and reservation of the Sacrament, including Corpus Christi processions, illegal in the UK and cause for raised eyebrows at minimum in the US. However, even at its peak, the movement was small and distinguished from "moderate" Anglo-Catholicism, which has since moved into the Anglican mainstream.
In addition, as a small and eccentric minority, it carried other baggage: it attracted people with actively gay lifestyles, occultists, and, at the time of the Spanish Civil War, fellow-traveling Stalinists. Although there are some holdovers and sympathizers even now, it's primarily a historical curiosity (one historian calls it a "museum piece"), and although it might provide an amusing digression in a Church history lecture, I don't think it can be seriously considered an important part of "Anglican patrimony".
This leads me to the puzzling question of why the Ordinariates would choose to use a version of the Anglican Papalist missal from 1905 as the authorized liturgy. On the other hand, in one of his few official utterances, Msgr Steenson has said,
Some of our clergy want to learn also how to celebrate according to the Extraordinary Form of the Roman Rite. They are certainly encouraged to do so, under the provisions of Summorum Pontificum and under the supervision of the local bishop, to assist in those stable communities that use the Extraordinary Form. But as the Extrordinary Form is not integral to the Anglican patrimony, it is not properly used in our communities.But both the Latin mass and the 1905 English Missal, which forms the basis of the Ordinariate liturgy, were used by Anglican Papalists. The 1905 Missal was no more authorized in Anglican denominations than the Latin mass -- strictly speaking, neither is part of an Anglican patrimony -- or if either is, how do we distinguish it from other accepted parts of Anglican Papalism, like the occult?
I'm inclined to say that if Ordinariate leadership wants to salvage the outcome of Anglicanorum coetibus, a good start might be to rethink "Anglican patrimony", lose the Anglo-Papalist craziness and the 1905 Missal, and go to something much more like the 1979 Rite Two.
