So, then, perhaps we can't get away with calling the NO sort anything but simply Catholic in conversation with them.
But if they aren't Catholic, why would you do that? I understand the unique problem. These are not Lutherans, nor let's say Anglicans, claiming to be Catholic. They know the term, Anglican, or Episcopalean. They may try to use, Catholic, but they understand, perhaps, the history of the Church of England.
What you have, here, is an apostate Church. When that occurs, the Church becomes something else. Even as an heretical Church, Catholics never historically had a problem identifying those who WISHED to be called Roman Catholic, as something else - such as Arian.
You can examine the writings of Athanasius, for example. His complaint is not with Roman Catholics. His complaint is with Arians. But who were these Arians? Where were the found? And so on for various heresies.
Consider the history, here.
I don't like bringing these questions down to the level of a 'practical matter'. But you'd be surprised, as a 'practical matter', how dissatisfied some of the most supportitive parishioners of these Roman Protestant parishes are. If you say to them, this is Roman Protestantism, and do it face to face, you might discover surprising agreement. Even without prompting, they themselves may begin to describe the latest songs, the ad hoc innovations, the utter irreverence with the word - Protestant. I've seen this, myself. And I just can't see how truth is served, or how others are served who need to be, by a political correctness that is a great distance from any legitimate concerns for simple courtesy. People very much appreciate honesty. You have to give these folks some credit for being able to appreciate their situation, and how messed up it is. They see all this stuff, too. I think Catholics, perhaps some, tend to forget that.