“If a Christian teacher says that ‘false teaching’ is occurring in a congregation of which he is not a member, would this be considered ‘judging’? Would it violate a church’s ‘autonomy’?”
There are actually two elements of this question that require consideration.
Somehow, many folks assume that all judging is wrong (yet they are not reticent to judge those whom they feel are judging). But all judging is not wrong. Hypocritical judging is wrong, i.e., condemning someone of the very thing that you are practicing (Mt. 7:1-5; Rom. 2:1ff). Superficial judging, i.e., judging on the basis of mere appearance, is evil as well (Jn. 7:24a).
On the other hand, Jesus commanded us to judge righteous judgment (Jn. 7:24b), which is a judgment (pronouncement) consistent with Scriptural teaching.
Paul rebuked the Corinthian Christians because they were flaunting their differences before unbelieving authorities, rather than “judging” these matters within the confines of the congregational environment (1 Cor. 6:1ff).
And so, a certain type of judging is not only not wrong; it is positively required.
The second aspect of the question deals with what one may or may not criticize relative to the affairs of a neighboring congregation.
If the subject under consideration has to do with an issue of mere expediency, it is not appropriate for the members of one church to be harshly negative toward the activities of another congregation. Expediencies are matters of personal judgment, and ought not to be targets for hostile barbs.
Having said that, the notion has evolved in the thinking of many that a congregation may practice virtually anything it pleases — no matter how much of a departure from the truth — and no one, who is not a member of the congregation, is at liberty to offer any censure. Such a view is far from the truth.
When Paul wrote First Corinthians to the church in Corinth, he was living in Ephesus (1 Cor. 16:8), where he labored for approximately three years (Acts 20:31). While in Ephesus, the apostle received reports of various happenings in Corinth. Accordingly, he wrote First Corinthians to address problems within that church.
That congregation was divisive in spirit (1:11ff). The Corinthian saints retained a fornicating brother within their fellowship (5:1ff). Some were litigating their differences before heathen judges (6:1ff); others were abusing spiritual gifts (12-14). Some of them even denied the future resurrection of the body (15:12).
It apparently never occurred to Paul that he was “meddling” in the affairs of a church of which he was not a member.
A Christian has the right to oppose error — wherever it may be. We would respectfully suggest, however, that it is not a reflection of maturity and balance to virtually consume one’s time in monitoring the problems of other congregations. When one virtually makes a career of “policing” the brotherhood, he reveals that he does not have a responsible view of what Christianity is about.