I think it is fair to say that there are some (please note the emphasis on some) Anglo-Catholics who are hypocritical in their faith or practice. That is, they align themselves formally with the Anglican church despite explicitly rejecting its formal doctrine and defying its disciplines around worship. (This is also true with Anglicans at other extremes, of course).
I have some sympathy for them in that they are in an awkward position, in that there might not be a church in which they could be members with complete integrity, but nonetheless this is the path they've chosen to pursue.
I think the question is, do they then define their denomination, such that the fact that these people exist is enough to cause you to avoid the denomination? Do you not find hypocrites in every denomination?
I would argue that the question, "Should I be an Anglican or a member of another church in communion with Canterbury?" shouldn't come down to whether or not there are some Anglicans who test the extremes; but to whether the formally defined doctrine and worship of the denomination is one to which you can freely assent.
I don't disagree with much of your comments here; it's all fair. But there are a couple of things to consider: If we're just talking about members of the laity or some stray clergy; that's one thing. But there are bishops who hold some of these views as well (at least, that's what it looks like). Paul commands us in Galatians to "accurse" those who teach a contrary Gospel: "But even if we or an angel from heaven should preach to you a gospel contrary to the one we preached to you, let him be accursed."
It's this very same view that the Reformers pointed to when justifying their decision to break communion with Rome, rather than stay and protest. The Book of Concord, the Lutheran confession, states this explicitly in a couple of places. If we should be tolerating a Gospel that is not "justification by faith alone" than why did we ever break away from Rome in the first place? We should have just stayed and tried to reform from within.
If rejecting justification by faith alone is tolerable, then what else is tolerable? It seems as though anything is tolerable, except for radical liberalism, and even that took far too long for orthodox Anglicans to break away from. I'm an advocate for a big doctrinal tent, but a line has to be drawn somewhere, and I think drawing it at justification is fair, since that's what the Reformers did (in the beginning, they squabbled later on, no doubt) and that's what Paul commands.
This, of course, is just my opinion. I'm sure many Anglo-Catholics hold views on justification I might disagree with but would feel comfortable communing with. Some, however, do not.
Further, Anglo-Catholicism in and of itself is quite disingenuous on certain issues, such as their reinterpretation of the 39 Articles, which plainly advocates for justification by faith: "We are accounted righteous before God, only for the merit of our Lord and Saviour Jesus Christ by Faith, and not for our own works or deservings. Wherefore, that we are justified by Faith only, is a most wholesome Doctrine, and very full of comfort, as more largely is expressed in the Homily of Justification.
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Anyone who reads that and tries to suggest it presents some other view is delusional, dishonest, or really confused. I'm not sure how anyone could reasonably read "faith only" and hear "faith plus works."