I think the point of the prohibition you are talking about can be summarized in a different injunction: "minding your own business".
In other words there are judgments that we have to make because they concern yourself and others, and there are judments which are really just butting into other people's business.
The injunction "not to judge others" is largely a Christian one and naturally therefore refers to butting into matters which are properly a concern only between a person and his God and is nobody else's business.
To pick on several controversial examples:
The lifestyle of a homosexual is certainly no business of someone who is not homosexual, unless it is a close family member (like a heterosexual partner). The more difficult exception is the case that the person is clergy in a religion that considers homosexuality a sin rather than a characteristic of birth, since in this case there is a conflict of fundamental beliefs.
Once a man beating his wife was considered nobody's business but fortunately this attitude is changing. Women are no longer considered property and it becomes the business of everyone to uphold the rights of women against abuse.
Yes employers must judge employees, but the common use of inappriate criteria has made judgement based on issues which are none of the employer's business (like religion) unacceptable and illegal.
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