"You've got it about right. But you are leaving out the fact that Scripture enjoins us from judging each other (Mt. 13:24-30, Rom. 14:4, Rom. 14:10-13)."
Lets take a look. For the sake of brevity, I won't print out every verse that you can read in your own Bible.
I've been meaning to get to this for awhile, but lacked time and energy until tonight. Rather than the assumption that 'Scripture enjoins us from judging each other', the opposite is actually true. Christians are not supposed to be able to tell whether someone else is a believer? In the Matthew parable, Jesus is talking about tares being planted among the wheat.
Tares aren't wheat. And nothing in the parable proves that a 'wheat' can't tell who is a 'tare'. Read down past Mt. 13:24-30 and you find the disciples asking for the parable to be explained-please read Matthew 13:36-39.
"4Who are you to judge the servant of another? To his own master he stands or falls; and he will stand, for the Lord is able to make him stand." Romans 14:4
This verse needs to be read in context-please read Romans 14:1-4:
And then Romans 14:10-13
Again, there is an admonition for one believer not to judge the faith of another believer. Believer. Not unbeliever. The rest of Romans 14 makes this clear. I am not to judge, for example, a brother who believes differently than I do about Sabbath days, or what he can or can't eat or drink (Doug, do you eat shellfish?). And he, my brother in Christ, is not to judge me for my beliefs. Clear as glass.
Paul warned the Corinthians to be on guard against false Christians, warning them to judge who is and who is not a believer-please read 2 Corinthians 11:12-15
John judged who was or wasn't a Christian: Please read 2 John 7-11.
Finally, Jesus Himself often made clear the difference between believers and unbelievers-please read John 10:25-28, and then Matthew 7:21-23
To sum it all up, please read 1 Corinthians 2:10-16 Maranatha!