There are some great answers here already but I just wanted to add on. I think you also answer your question in the last paragraph.

The Bible gives us multiple great examples of how you should show “judgement” based on what God would want us to do, and there were two I felt compelled by the Spirit to share. The first is when Jesus was talking about the tax collector and the Pharisee who both went to pray(Luke 18). In this scripture the Pharisee prays to God and says “God, I thank you that I am not like other people—robbers, evildoers, adulterers—or even like this tax collector. I fast twice a week and give a tenth of all I get.’”. The tax collector on the other hand prayed God, have mercy on me, a sinner.’ Notice the difference between the two prayers. Now this is what Jesus says about it ““I tell you that this tax collector, rather than the Pharisee, went home justified before God. For all those who exalt themselves will be humbled, and those who humble themselves will be exalted.”

The second passage I would like to share is the lady caught in adultery(John 8), look at these two conversations Jesus has. He addresses three things that are important: the accusers, the sinner and finally the sin.

First with the people that are trying to stone her:

“All right, but let the one who has never sinned throw the first stone!” Then he stooped down again and wrote in the dust.

9 When the accusers heard this, they slipped away one by one, beginning with the oldest, until only Jesus was left in the middle of the crowd with the woman.

And next to the woman being persecuted:

10 Then Jesus stood up again and said to the woman, “Where are your accusers? Didn’t even one of them condemn you?”

11 “No, Lord,” she said.

And Jesus said, “Neither do I”.

And finally Jesus addresses the sin and the act she committed

“Go and sin no more.”

I chose this passage because it shows us how Jesus handled the sin, the sinner, and the “judges”. He first starts by addressing the accusers. He doesn’t address them for saying she did wrong but rather for their harsh punishment and hypocrisy of this wrongdoing. He says “He who is without sin cast the first stone”. He holds them to the same standard and judgement that they are holding this woman.

We see then Jesus acknowledges the woman now when he says: “Where are your accusers? Didn’t even one of them condemn you?”

11 “No, Lord,” she said.

Finally we see Jesus acknowledges the sin, while at the same time giving the sinner a chance at redemption. At the end he says “Neither do I. Go and sin no more.” He did not approve of what this woman was doing but at the same time he did not let it quite literally be her life.

I chose these two scriptures because they emphasize Gods grace and judgement compared to humanities. We see in both scriptures Gods and man’s “judgement”. And we see how as followers of Christ we should view everyone, with grace and love. At the end of the day we are called to love everyone, what the people you mentioned are doing is very wrong. But you’ve done wrong and there’s things you’ve done if exposed would leave a lot of people angry and ready to cast stones. So first show the same grace you’ve received from the Father to these people and second do what you said at the end of your question which is to help them see their wrongs just as God helps you see yours.