How to respond to the sins of others

If you see a man who has sinned and you do not pity him, the grace of God will leave you. Whoever curses bad people, and does not pray for them, will never come to know the grace of God.
(St. Silouan the Athonite, Writings, VII.4, VIII.6)

Love sinners, but hate their deeds, and do not disdain sinners for their failings, so that you yourself do not fall into the temptation in which they abide… Do not be angry at anyone and do not hate anyone, neither for their faith, nor for their shameful deeds… Do not foster hatred for the sinner, for we are all guilty… Hate his sins, and pray for him, so that you may be made like unto Christ, who had no dislike for sinners, but prayed for them.
(St. Isaac the Syrian, Homily 57,90)

Find evil in yourself and not in other people or things, wherewith you have not learned how to relate properly. This is how a child relates with fire or a knife: he burns himself, he cuts himself.
(St. Sebastian of Karaganda)

A man may seem to be silent, but if his heart is condemning others, he is babbling ceaselessly. But there may be another who talks from morning till night and yet he is truly silent, that is, he says nothing that is not profitable.
(Abba Poemen in the Sayings of the Desert Fathers)

A brother asked an elder: If I see my brother fall into sin, is good to hide him? The Elder answered: When, out of love, we hide the sin of our brother, then God also hides our sins; but when we show our brother’s sin before others, then God also makes our sins known to people.
(Ancient Patericon, 9.9)

Do not lose your temper with those who sin. Do not have a passion for noticing every sin in your neighbor and judging it, as we usually do. Everyone will give an answer for himself before God. Especially, do not look with evil intention on the sins of those older than you, with whom you have no business. But correct your own sins, your own heart.
(St. John of Kronstadt, My Life in Christ, I.6)

If you see your neighbor in sin, don’t look only at this, but also think about what he has done or does that is good, and infrequently trying this in general, while not partialy judging, you will find that he is better than you.
(St. Basil the Great, Conversations, 20)

One who strictly prosecutes the misdemeanors of others will find no condescension toward his own.
(St. John Chrysostom, On the Statutes, 3.6)