Regarding your interpretation of Matthew 7:1, you seem to render the context to imply that this verse is broadly speaking against judgments of any kind. We sin so we can’t judge sin in another. But the context of Matthew 7 reveals that Jesus was mainly concerned with hypocrisy and not sin in general. “You hypocrite, first take the plank out of your own eye, and then you will see clearly to remove the speck from your brother’s eye.” (Matthew 7:5) Also in the same sermon 7:15-23 Jesus warns his disciples to watch out for false prophets, that we ought to judge these by their fruits i.e. actions.
You have a unique interpretation here. Most scholars see Matt. 7:1-2 as a general warning against judging others, saying we shouldn’t judge others unless we want to be judged the same way. They see the Lord’s use of the word hypocrite as applying to those who insist upon judging others when their own sins are piling up around them. His use of speck in referring to the sins of another and plank in referring to their sins shows the extent of their hypocrisy. And in Matt. 7:15-23, Jesus said we can recognize false teachers by their fruit. He wasn’t saying to judge them by their fruit.