Okay, now that you've shown us how non-believing Jews handled their judgments, and since we're moving on to the evangelical part of following Christ, can you share how Christians are to judge/assist one another?
I didn't know your post was for advice, it looks more like you made up your mind about most Christians graphs and all, didn't leave much room for discussion or dispute, so I had some fun, although I don't recall the phrasees( non believing jews I guess?) having a sense of humor in the bible...
But alright.
We are to rightfully judge for one. So come into a situation slow to anger and quick to listen. Access and discern the circumstance and measure it up with the Word.
Now that you gather your info, and measured it to the Word, now it time to deliver the message. How depends on individual circumstance, and it also depends on your heart in the matter. You may have the Word, but the wrong approach will taint your testimony. So examine your heart, are you telling them to bring them closer to God or for your own benefit. Would you tell it despite how you may look? How would you want someone to approach you with a Truth you may not like? Sometimes it looks like tough love, and sometimes it's a nice hug.
So you said your piece, how is your follow-up? Are they receiving it? Then good keep pouring into them. Were they not ready to hear it, that's fine leave them be and pray for them. What didn't they understand? Expound on it further. Can't you? ok, tell them you don't know it all but tell you testimony, how He is instrumental to you. Be patient with them with an understanding that God is patient with you, and teach with full knowledge of the end goal, to point them to God, and God will take it from there.You are looking to service THEM, they don't serve you. They are for GOD to work on, not you.
So when you pronouncing them who they are as a sentence with no intention to be either patience, to teach them, or bring them closer to Truth,you are not assisting or bringing light to anything but your lack of ability to point people to Christ.
Paul wrapped this up neatly in 2 Timothy 4:2 (ESV)
Preach the word; be ready in season and out of season;
reprove, rebuke, and exhort,
with complete patience and teaching.