I judge people who are behaving stupidly or immorally, and I expect them to judge me the same way. I'm not asking for special treatment. If I'm doing something stupid or immoral (and I find the two often coincide) then I think I would want people to judge me, and push me to get my head on straight and stop doing those stupid or immoral things.
Maybe when people say "Don't judge me" or "Don't judge others" they mean something different than I do by "judge." I suspect they mean "don't assume you know enough details about the situation to have an accurate reading of what's going on" or "don't think you're better than people, consider some of the things that you've done yourself" or simply "don't be hateful." I like this idea:
And while I agree with being kind and taking care not to assume too much or be arrogant, I don't think that's all there is to "judging." I think some people take the "no judging" thing to the point of "no thinking" or "no standards."
When you see immorality, or just plain stupidity, you should point it out. People won't necessarily change, or listen to you at all, but it's not wrong to stand up for what you think is right, and similarly, there's no reason to fear other people holding you to the same standards. I do judge people, and I expect them to judge me in return. Not hate me, not scream at me, but to tell me when they think I'm in the wrong. I'm fine with that.