iIs it a sin to not tell someone that they are living in sin?

Here is how an atheist sees it. Pen Jillette said, "How much do you have to hate somebody NOT to prosyletise them? If I believed that a truck was going to hit you, but you did not believe me, there would be a certain point where I would tackle you."

Now there speaks a sensible atheist who understands why Christians speak out to warn about sin and God's judgment of it, which will eventually be hell, for unrepentant sinners.

Scriptures, you ask? Lots of them - all the ones where Jesus warned people of sin, especially in areas where they prided themselves in being spiritual. Two examples, otherwise I will take hours to answer;

"If you do not believe that I am the one I claim to be, you will indeed die in your sins" John 8:23-58.

Then read Luke chapter 16 where religious people who loved money sneered at Jesus, who then spoke of the rich man dying and ending up in torments in hell, and Lazarus the beggar who died and found himself in bliss in the Bosom of Abraham.

Jesus set the example by speaking most plainly about sin to people who prided themselves in being religiously correct. For the rest of the time, He felt empathy for the people who suffered the bad shepherding of those leaders. He encouraged them to have more faith and to leave sin behind. Take the woman caught in adultery, at the start of John chapter 8. Jesus dealt with her accusers, got them slinking away in shame by showing none of them were fit to throw the first stone because they were equally sinners. Then He did not accuse the woman but told her to leave her life of sin.

It is HOW we tell people that matters, and WHO we tell - we are not like Jesus, who could read hearts and minds (the divine prerogative). We are equally sinners as are the people we would warn about sin. This calls for humility on our part. There, but for the grace of God, go I. AiH

There is a difference between being a nosey busybody and respectfully pointing out the way to God. We don't have to point out individual sins - but we do feel impelled to help people understand what a wonderful God we serve. We do not convert people - the Holy Spirit does.

Mathew 7:1-5. ( the following is paraphrased) When you are free of sin then you can judge someone else's sin. Until then, work on your own sin. In other words, mind your own business.

It's a sin to be a judgmental holier-than-thou nosey gossipy busy-body.

Let us pray: O Lord, deliver us from do-gooders. Amen.

there is no sin but judging others lifestyles may be obtrusive

No