First of all we need to realize there are two words that relate to judgment. The first one means "to cast a sentence," like a judge would do in court. Only God the Father has the right to cast a sentence about our eternal destiny.
The second word for judging is "to evaluate or examine." Our Lord Jesus Christ told us that we would know them by their fruit. This requires a judgment or evaluation according to Scripture. The Word also tells us that we don't judge those outside the church but we are to judge those within the church. We have a responsibility to evaluate one another and hold one another to the faith that is in us.
Gal 6:1(ESV) Brothers, if anyone is caught in any transgression, you who are spiritual should restore him in a spirit of gentleness. Keep watch on yourself, lest you too be tempted.
The righteous judgment released by the believers: However, in the end God will use the saints to judge all things.
1Co 6:2-4(ESV) Or do you not know that the saints will judge the world? And if the world is to be judged by you, are you incompetent to try trivial cases? 3 Do you not know that we are to judge angels? How much more, then, matters pertaining to this life! 4 So if you have such cases, why do you lay them before those who have no standing in the church?