Conscience is a judgment of reason by which the human person recognizes the moral quality of a concrete act.We absolutely need to judge concrete acts (behaviors) in order to grow. To judge well we must have a well-formed conscience to better know ourselves and to love others.
How does this look in real life? Let's say there is a teen attending Mass in a revealing outfit. It is correct to judge objectively that the outfit is revealing and not appropriate for Mass based on the expectation of semi-formal wear, "Sunday Best." My judgement allows me to dress properly, avert my eyes, to say a prayer for the young person, and to give a warm welcome, being rightfully pleased by his or her attendance. I can't judge her intent or the state of his soul, which God alone judges. If I grow in relationship with the teen over time, we may discuss appropriate dress.
If "don't judge" means to give benefit of the doubt and to be loving, courteous, and respectful, I'm in. If it means, "There is no right or wrong," I disagree. If it means, "I'm shutting down discussion," reconsider. If it means, "I want to do what I want to do and I want you to approve," then that conscience is immature, limiting one's ability to love others and judge reasonably.