Correct Idea: We all sin, therefore no one can judge another person.
Correct Interpretation: I am a sinner, therefore I have no right to assume I am inherently better, purer, or closer to Allah than others.
Incorrect Interpretation: I am a sinner, therefore I have no right to insist on, suggest, or advise others on the right way to do things because that would be hypocrisy.
Note 1: The confusion people have is the ambiguity in the term “judging” in the English language. To judge something can mean to internally assess or it can mean to pronounce a ruling as in what a judge does in court. A big component of all the arguments the English-speaking Muslim community has on “judging” rides on this ambiguity, where one side insists that “we shouldn’t judge” in the sense of internal assessment and the other side insists that yes, Islam does provide judgment, i.e., literally ahkam, and back and forth. And of course there are those confused individuals who think that all judgment in all senses of the word, even judgment from God Himself, is illegitimate. [face palm]
Note 2: It is false piety to keep silent and refrain from advising others on the excuse that “I am a sinner, therefore who am I to speak?” Advising others is based on sincerity, not on arrogance, i.e., that “I am better than you,” and not on bashfulness, i.e., that “I am a sinner and should keep quiet.”