Saw a very good Charlie Kirk short on this topic recently. The misuse of "he who is without sin cast the first stone" being used to try to convince people not to judge or call out sin. But he brought up the next part, which is often left off, "go and sin no more".
On a similar topic, he had a good one on moral relativism, and how dangerous it can be.
The gist, there is universal truth, there is universal good and evil.
Yes. I don't think it's the point Adcoop is making, but, yeah, the Bible doesn't "never judge anyone".
The passage "Judge not lest ye be judged" does NOT mean "don't draw conclusions about people's behavior based on biblical principles". It uses the word "judge" in the sense of condemning a person to final judgment. Christians are certainly called to be discerning and that involves judging...identifying certain behaviors as sin. We are not called to condemn people...in the sense of passing final judgment. That is God's duty alone. In the passage you are referring to of the woman caught in adultery, the Pharisees wanted to pass final judgment and stone her to death. It would surely have been fine to identify her action as sin and condemn the sin and call her to repentance. We are cautioned by Jesus not to "cast stones" because before God we are all sinners deserving of the ultimate judgment.
But surely, one of the main functions of Christians in the world is to identify and decry sin (letting our line shine). As you suggest, too many people (even some professing Christians) overlook any nature of gross sin, wrongly citing "judge not lest ye be judged" and applying it as "hey, who am I to say what's sin and what's not?".