In 2012, Msgr Steenson, the first OCSP ordinary 2012-15, issued a pastoral letter clarifying Rome's position on how the Tridentine mass relates to Anglicanorum coetibus. Intrestingly, it no longer appears on the OCSP website, but I was able to find the applicable part of its text here:
I don’t understand the connection between the groups you blog about (Anglican/Catholic hybrid) and those who believe Vatican II liturgical changes were a mistake. I see the political advantage: two groups, each wanting to worship in their own way. However, if you gave truth serum to someone from the Latin mass group, they would tell you that the new mass isn’t “really” a mass, that the only way to raise their children Catholic is to take them to Latin masses, and their pipe dream is to revoke Vatican II, liturgically at least, and make the Tridentine mass universal. And what is the Anglican tradition but an early version of the Vatican II changes? The Tridentine mass was created to be a bulwark against Protestantism. So I don’t really “get” why these groups are forming even tentative alliances.
The other contrast between these two groups regards the priests. The priests who want to celebrate Latin mass in each diocese are firmly embedded in the diocese hierarchy and their sole obedience is to their own Bishop. And these priests are very careful, no matter what the laity think, to speak respectfully of Pope Francis, and they only celebrate the Latin mass at the directive of their Bishop. It does seem a huge mistake to ever make the chain of command for Anglican groups separate, rather than folding them into existing dioceses.
I came across your blog because a Latin mass Facebook page posted the Church Militant link about those nuns in Texas. And recently I came across a post in a private Latin mass FB group where someone from the Anglican camp was putting out feelers (see screenshots). She did not get any takers but it seemed odd that she thought she might.
We have therefore asked that the congregations of the Ordinariate follow this direction. 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. The Ordinariate will remain focused on bringing Christians in the Anglican tradition into full communion with the Catholic Church. We also are pleased that the Church has provided for the continuing use of the Extraordinary Form, particularly as a pastoral response to traditional Catholics, and regard all of this as a well-ordered symphony of praise to the Blessed Trinity.I think the visitor raises a valid point. Bp Lopes has at least leaned in the direction that the "Anglican patrimony" consists almost entirely of the 17th-century BCP liturgy, although it's worth noting that its own survival is due to accident -- an attempt to revise it in the 19th and early 20th centuries stalled for lack of consensus. And it's definitely worth noting that Episcopalian and Church of England interior furnishings, as well as Catholic-style vestments, are a 19th-century innovation. Altars, reredoses, candles, crucifixes, albs, surplices, cottas, copes, chasubles, incense, servers, and the like date only from the 1840s and later. Church of England and Episcopal interiors prior to then looked much more like modern Baptist interiors, with priests normally wearing just black cassocks and sometimes academic gowns while preaching.
Clearly what we've been observing here is that enthusiasts of the "Anglican patrimony" share perhaps more with sola sciptura types than they do with truly devout Catholics -- they show the same willingness to freelance what the Anglican patrimony consists of as scriptural fundamentalists do in interpreting the Word. To the extent that traddie enthusiasm for the Latin mass and the "Anglican patrimony" are affectations and inauthentic, the two groups certainly share a lot.
But the visitor is also correct in seeing the two groups as more or less separatist, and especially with the Anglicans, at risk for trying to set themselves up as a separate and overlapping jurisdiction, since they have their own bishop. I would say the centrifugal tendency is there in both groups, but the visitor does see that the Latin mass is done entirely in the context of the diocese.
This was also the case with the Anglican Use Pastoral Provision, and the largest OCSP parishes came from diocesan jurisdictions under that provision. Even then, though, the relationship of Our Lady of the Atonement with its archdiocese was not smooth.