To begin with, isn't arguing that we should not judge in itself a judgment? If it is, then isn't the idea intrinsically contradictory? Doesn't it pull support right from under itself? It is simply an entirely untenable position, especially with questions of God or right and wrong. If God doesn't judge, or at least expect us to act certain ways, then why did he bother about those pesky Commandments?
That is perhaps the most critical point in having to make judgments. From that idea, we surely must see that the concept goes all the way down. It would be awfully hard to be a good parent if you could never judge the actions of your children. Society could never make the first law for the simple reason that laws make judgments. Indeed if judging is wrong then how might I ever decide which contractor to repair my home or car, for in the act of choosing Mechanic Sam ahead of Mechanic Kyle I have judged Sam's talents superior to Kyle's. But if sort of judging is wrong, then my car shall never get fixed. No; we simply must judge actions (and histories and abilities) if we are to get on in this world.
It is interesting that those who assert that we cannot judge never condemn judgment over things they believe good. They encourage it in fact. They say things like, we should accept everyone no matter what. Well, accept me and my judgmental ways then; of course, they won't do that. I can't help but think it's hypocrisy, however inadvertently or unintentionally it may be done. If judging is wrong, then judgments about what is good are as invalid as judgments about what is bad. At that point, as with picking our mechanic, we couldn't get anything done because even a good judgment, would be, by obvious inference, out of the question.
The bottom line is that non-judgmentalism is an impossible scientific, philosophical, theological, or even merely practical position to hold. But I bet that won't stop the no judgment folks from judging my words here, will it?