I will offer two thoughts on this trajectory I've noticed. First, extending on the pure/impure distinction I mentioned in the above paragraph, I will relate this to Article 26 and the traditional and historical Anglican norm. Secondly, I will discuss a concept I call "guilt by association" which I have noticed in many of the people I've spoken with having these separatistic tendencies.
First, beginning with our Church's teaching on the nature of wicked ministers, which is contained in Article 26. This follows the traditional, Augustinian paradigm of a "wheat and tares" Church, that meaning that the visible Church will be comprised of both godly and wicked people until the return of Christ (this is not to be confused with the "invisible Church" or the Church as God sees it).
XXVI. Of the Unworthiness of the Ministers, which hinders not the effect of the Sacraments.
Although in the visible Church the evil be ever mingled with the good, and sometimes the evil have chief authority in the Ministration of the Word and Sacraments, yet forasmuch as they do not the same in their own name, but in Christ's, and do minister by his commission and authority, we may use their Ministry, both in hearing the Word of God, and in receiving the Sacraments. Neither is the effect of Christ's ordinance taken away by their wickedness, nor the grace of God's gifts diminished from such as by faith, and rightly, do receive the Sacraments ministered unto them; which be effectual, because of Christ's institution and promise, although they be ministered by evil men.
Nevertheless, it appertaineth to the discipline of the Church, that inquiry be made of evil Ministers, and that they be accused by those that have knowledge of their offences; and finally, being found guilty, by just judgment be deposed.
The first part of this article establishes that the visible Church is comprised of both evil and good. This is due to the nature of mankind and the situation of the Church in an imperfect world. Moreover, due to the "mixed" nature of the visible Church, sometimes these wicked people will be in charge or cure of souls. However, these ministers (and all ministers) do not preach the Gospel or administer the Sacraments in their own name but in Christ's. It is for this purpose that the ministry of a wicked person is not negated because of his own name but it is effective because he works in Christ's name, this is obviously referencing the efficacy of the Sacraments. The problem of course is that the separatist is not comfortable with the mixing of good and bad (I use the word "comfortable" cautiously here, no one should be truly comfortable with this but the orthodox believer notes that the wheat and tares will share the same space until Christ's return). The separatist ideally wants a pure Church, a concept which is not attainable in this life.
Some may say that the second part of the article requires that these ministers be deposed. Yes, it is required that "inquiry be made of evil Ministers", meaning that the believer needs to notify proper authority of these said ministers and leave the act of deposition to those in proper authority. The article does not authorize or require lay Christians to depose such ministers but to notify the authorities. Neither does it discuss what Christians are to do if an evil minister is not deposed.
The second point that separatists like to make is that of "guilt by association". This is the idea that individual Christians are personally responsible for what other Christians in their denomination, particularly leaders, have done, will do, or are doing. For instance, because I am a communicant member of an Episcopal parish, the separatist will (and have) accused me of being a godless liberal. This idea is completely ludicrous. Moreover, the separatist is not immune from this criticism himself. The teaching of the Bible is that we are responsible for our own actions and not those of others. We are to be judged for what we have done not for what our brother or sister has done. Now, if someone is in a situation where unbiblical teaching occurs or an ungodly person presides over a service or whatnot and the believer does nothing, this is something that he will be held responsible for, because it is the duty of the believer to stand up against false teaching.
The last point to be made is that being in relationship to another person (ecclesiastically speaking) does not necessarily convey complete acceptance of them or their teaching. To give an example, many in the ACNA are against the ordination of women, as a primary issue, yet they are in communion with and relationship to others who ordain women. (As an aside, by logic of the "guilt by association" argument, these people are just as guilty of sin, in their theological paradigm, as the bishop who ordains women.) If you were to approach the bishop of the Anglican Diocese of Fort Worth and accuse him of ordaining women, he would probably laugh at you. Yet, if you follow the separatist's logic, he is guilty of this, even though he has never ordained a woman. Hopefully you can see how ridiculous this type of logic is. Being in relationship to another person does not make you responsible for their actions or beliefs nor does it convey your complete acceptance of them.
I offer in closing the remarks of J.I. Packer regarding "guilt by association" in response to the call of the late Martyn Lloyd-Jones for Evangelicals to leave the "impure" Church of England and start a new, doctrinally-pure Church:
"I lived as some of you lived, through the era in which the late great Martyn Lloyd-Jones was telling us Anglicans from where he stood that we all of us ought to leave the Church of England. He had two bad arguments. He was a great man, but great men can be enmeshed in bad arguments. Bad argument number one was that if we stay in the Church of England we're guilty by association of all the theological errors that any Anglican may be propagating anywhere at all. To which of course the answer is rubbish: on that basis Paul would have been guilty of all the errors that were abroad in Corinth, in Colossae, in the Galatian churches and the Thessalonian church and elsewhere -- and of course he wasn't guilty of any of that, and why not? Simply because he entered into the discipline of debate and wrote pastoral letters to them too put them straight. As long as we are free to raise our voices against the errors and seek to correct them from within we are not guilty of them. We are negating and refusing the error, we are not acquiescing in it, we are not guilty of it. It was a sad thing that a great mind like that of the late Dr Martyn Lloyd-Jones should have ever toyed with an argument as bad as this one.
"Secondly he said, 'Don't you see that the times call us to leave all the doctrinally mixed congregations and form a pure new one.' And I and others looked around and couldn't see that the times called us to do any such thing. We asked what do the times call us to do? And it seemed clear that the times called us to stay put and work for Reformation, renewal and fresh life in the church that has this rich heritage. So when people used to ask me why are you in the Church of England when the Church of England is in such a mess today I used to reply, 'I'm in the Church of England today for the sake of what under God it might be tomorrow.'"