A lot of people think that Jesus' commandment against improper judgment (in Matthew 7:1) is actually forbidding us to question other people's salvation no matter what they do. That is not true.
In the first place, people who say that are taking His words out of context. The context is hypocrisy, not judgment. How can we condemn a person as evil if we do the same thing? It doesn't matter if no one sees it--God sees it; and that should make us tremble in humility. But we can and should discern who is on our side, and who is against us.
Jesus said, "Beware false prophets, which come to you in sheep's clothing, but inwardly are ravenous wolves." (Matthew 7:15) If someone says to you, "Beware of the Dog"; what are you going to do? If you believe that they have good reason to say this, then you would be very watchful to be sure that the dog does not catch you unaware. We know Jesus had a good reason to say this (or do we?), and therefore we must also be very careful, watching with the best of our ability to make sure that these "wolves" do not catch us unaware.
How will we know what is a wolf and what is a real sheep? Jesus said, "Ye shall know them by their fruits. Do men gather grapes [from] thorns, or figs [from] thistles?"--No--"Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit. A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit. Every tree that bringeth not forth good fruit [that is to say, every evil tree] is hewn down and cast into the fire [Rev. 20:15]" (vv. 16-19). Now what does He mean by evil fruit?
Well, what did Jesus say was the reason that anyone who will go to Hell will be there? "This is the condemnation: that Light is come into the world, and men loved darkness rather than light, because their deeds were evil. For every one that [will be judged by God as] evil hateth the Light, neither cometh to the Light, lest his deeds should be reproved." (John 3:19-20) So then people who would rather pretend that they are righteous or justified in their iniquity, instead of turning away from their sins to the One Who can save them from their sins--those people are deliberately going to Hell, and we should not follow them nor align ourselves with them.
As Paul commanded us, "Be ye not unequally yoked with unbelievers:for what fellowship hath righteousness with unrighteousness? And what communion hath light with darkness? And what concord hath Christ with Belial [another name for satan]? Or what part hath he that believeth with an infidel? And what agreement hath the Temple of God with idols ? For ye are the Temple of God; as God hath said, 'I will dwell in them, and walk in them; and I will be their God, and they shall be My people.' 'Wherefore come out from among them, and be ye separate,' saith the Lord, 'and touch not the unclean thing, and I will receive you, and will be a Father unto you, and ye shall be My sons and daughters,'saith the Lord Almighty." (II Corinthians 6:14-18; Revelation 18:4)
Any attempt to include unbelievers as part of our Christian ministering crew requires us to de-emphasize the Gospel in order to close ranks. That not only is dangerous for the sheep, but it also prevents the births of new sheep. Wolves will often catch the pregnant sheep for two reasons: they can't run as quickly to get away, and they make a bigger meal. To bear fruit in Christ takes time, and if satan can stop people from becoming new converts, then he has won their souls for all eternity. It is very important to be able to tell who is really on your side and who is just out to get you, so that we can defend the pregnant sheep and nurture the other sheep until they are ready to bring forth fruit. I believe that's called "spiritual warfare"!!
A lot of people also define judging as condemning a person. The reasoning is that if the person is guilty, then we want them to be punished. But that is not the position I hold. If God were to punish everyone who deserved it, who would get to Heaven? Nobody; and since I'm going, I certainly am not going to stand in somebody else's way. They may exclude themselves, and I may recognize that they have, but I will certainly not encourage them to do so. That's satan's job, not mine.