Matthew 7 is the classical section that all non-Christians pull out every time they feel they are being “judged” by others, especially other people who claim to be living as a Christian. But of course Matthew 7 was not written to say that judgements should never be made, only that as Christians, we shouldn’t be “habitually critical or condemnatory of a speck of sawdust in a brother’s eye” (BKC, Matthew 7:1-6), and of course it does specifically say “brothers”, so this is flip flopping beliefs and faith in judgement. Not only does it say we should be restraint in our judgement but it is speaking about other believers, not other people in general.
Anyway, I came across this passage from “The Desert Fathers: Sayings of the Early Christian Monks“, which came from the book “25 Books Every Christian Should Read” by Renovare. I just loved how this Desert Father put it to his fellow believers.
A brother at Scetis committed a fault. A council was called to which Abba Moses was invited, but he refused to go to it. Then the priest sent someone to say to him, ‘Come, for everyone is waiting for you.’ So he got up and went. He took a leaking jug, filled it with water and carried it with him.
The others came out to meet him and said to him, ‘What is this, Father?’ The old man said to them, ‘My sins run out behind me, and I do not see them, and today I am coming to judge the errors of another.’ When they heard that they said no more to the brother but forgave him. 
I just love that. Such a great reminder of what Matthew 7 is really talking about, with great context into viewing our own sin and need for the forgiving grace that God provides.
 Renovare (2011). 25 Books Every Christian Should Read (Kindle Locations 839-843). HarperOne. Kindle Edition.