I'm very impressed -- that's a great question.
Many people don't understand the meaning of the Hebrew word our Bibles translate as "fool." They suppose it means a person lacking wisdom or insight, and is too stubborn or stupid to realize there is a God. In fact, the word used there is "moreh," which means "an APOSTATE who rebels against God." This is someone who once had faith, but who no longer chooses to believe; it is a willful act.
With regard to Matt. 5:22, Jesus clarifies that Scripture such as Psalm 53:1 does not give God's followers license to accuse atheists, pagans, agnostics, Muslims, etc. of being "moreh." He explains that whoever CALLS ANOTHER PERSON "moreh" will be punished, because God is the judge, not us.
Actually, if you step back and examine the context of Matthew 5 - 7, you'll see that Jesus is merely reiterating what already exists in the Mosaic Law. In the context of apostacy, the Law gave a penalty: the person was to be put to death either by stoning or strangulation (c.f. the Babylonian Talmud, tractate Sanhedrin), but ONLY if the following circumstances exist: 1) the person was heard blaspheming by at least two reputable men; 2) these men had never uttered or thought blasphemy and not been caught (c.f. laws re: "false witness"); 3) they had never committed any other transgression of the Law (also c.f. "false witness" Laws).
So while the Law contained the penalty, no one was worthy enough to accuse another of a transgression and exact the penalty -- EXCEPT if God Himself commanded it. This obvious fact totally escaped most Jews, but it explains why the woman caught in the act of adultery was not stoned.
Deut. 32:41, and other verses like it, makes it clear that God, and God alone, is the One who will punish apostates: "I will render vengeance to My enemies, And repay those who hate Me." Not Christians. Not Popes who say they stand in Jesus' place on earth. Not any of us. Period.
So you're right, those who condemn others will be condemned and more attention should be given to Matt. 5:22. I am not qualified to say whether these people are "real Christians;" at the very least, they have not read the Bible as carefully as you evidently have.