I'll talk about judging and the difference between that and discrimination. What do we judge and what do we not judge? Some people believe that when we develop Compassion/Lovingkindness, that we do not judge. However, if we look at wisdom, we see that wisdom is a discerning faculty of the mind. We cannot actually know what is skilful and what is not without some discernment. So we don't want to let go of all judging.
We want to lessen unbeneficial judgments and we don't want to let go of beneficial judgements. How can we do this? First, in order to keep the Compassion and Lovingkindness balanced with Wisdom, we have to learn how to separate the person from the actions, because we have to know for ourselves what is skilful and what is not. If a person is doing something unskilful, it is very important to know it is unskilful, otherwise we may join them in their unskilful actions. So we don't let go of beneficial judgements, this is part of Right Understanding, the first factor of the Noble Eightfold Path, understanding the Law of Cause and Effect, that all actions, speech and thoughts have results, and that all beneficial action, speech and thoughts will reap beneficial results and the opposite for the other.
We need to learn how to judge what is skilful, what is not and that also goes into discriminating what activity we spend our time with. It's the type of judgments based on things like what someone wears, their skin, etc., these types of prejudicial judgements we want to let go of because it doesn't really matter what a person wears or the colour of their skin or whether they like this type of music or that type of music or politics, etc.
This prejudicial judging, this judging of people from the outside, judging of people before we have heard their side of the story. Prejudicial judgements often come when somebody hears something from somebody else, some gossip and then they form some sort of judgement about another without hearing what the other person has to say about it or without investigating whether these judgements are true. These types of judgements we would like to let go of by reflecting that we don't know if that is true, so having an understanding that we would not like to get judged by others ourselves is helpful here.
How do we let go of this judging, this type of judging? By focussing on our similarities. All human beings are very similar in that we are subject to birth, aging, disease and death. We are separated from the things we like, we have to be with things we do not like. We don't get what we want. Developing Compassion/Lovingkindness helps us to let go of unbeneficial judging of others. Just as we do not like to get judged in a prejudicial way without someone hearing our side of the story, we try not to do that to somebody else. Keeping our ears open to what the other person has to say, not believing gossip and things without investigating whether it is true or not.
So, we don't want to let go of all judging. In order to be able to judge wisely we need an understanding to know what is worthy of judging and what is not. Understanding the ignorance in people helps us to understand this with Wisdom and Compassion.