Is there a converse of "judge not, lest you be judged?" One New Testament exhortation is "judge not, lest you be judged."

On the other hand, Romans 3:23 says, "For all have sinned, and fall short of the glory of God."

Is there any Christian sect, or school of thought believes the converse of the first line, something like "Judge and let yourself be judged?"

The core belief here would be something like, "You are a wicked, evil, sinful (wo)man--and so am I." (That's per the Romans passage.)

Put another way, is it possible to pass judgment on e.g. Adolf Hitler, knowing that "in his shoes, you or I might have done the same or similar things?" 

Some commenters below believe that a Christian can, and should judge the actions of others, while refraining from judging the "righteousness" of the person. Another opined that the admonition is against "hypocrisy," that the "converse" is OK, if you realize that "as you deal with my contemners, so with you my grace shall deal." Are either of these ideas in line with what the Scripture says?
Proverbs 27:17 says:


  As iron sharpens iron,
      so one person sharpens another.


Hebrews 10:24 says:


  And let us consider how we may spur one another on toward love and good deeds, 


And, the whole concept of mutual exhortation essentially reinforces the notion that 


  We who are strong ought to bear with the failings of the weak and not to please ourselves. (Romans 15:1)


So, in general, yes, the duty of one Christian to another is to exhort and encourage one another to live a life worthy of the calling we were given.  

This is more of a thing for believers to call one another too, however, rather than an injunction to tell the world to shape up.