Nation

Matthew 7 is where the quote comes from. I intentionally picked the Amplified Bible version (out of the 50+ English versions) because it "amplifies" in depth the meaning of what Christ said.
It says: “[a]Do not judge and criticize and condemn [others unfairly with an attitude of self-righteous superiority as though assuming the office of a judge], so that you will not be judged [unfairly]. 2 For just as you [hypocritically] judge others [when you are sinful and unrepentant], so will you be judged; and in accordance with your standard of measure [used to pass out judgment], judgment will be measured to you. 3 Why do you look at the [insignificant] speck that is in your brother’s eye, but do not notice and acknowledge the [egregious] log that is in your own eye? 4 Or how can you say to your brother, ‘Let me get the speck out of your eye,’ when there is a log in your own eye? 5 You hypocrite (play-actor, pretender), first get the log out of your own eye, and then you will see clearly to take the speck out of your brother’s eye."

If that's too much, here's the NIV (plain version of Matthew 7:1-5. “Do not judge, or you too will be judged. 2 For in the same way you judge others, you will be judged, and with the measure you use, it will be measured to you.

3 “Why do you look at the speck of sawdust in your brother’s eye and pay no attention to the plank in your own eye? 4 How can you say to your brother, ‘Let me take the speck out of your eye,’ when all the time there is a plank in your own eye? 5 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.

The Bible is full of examples requiring us to always be on guard / to consider / to judge the actions and words of others. One example is in 1 Corinthians 5:9-13... 9 I wrote to you in my letter not to associate with sexually immoral people— 10 not at all meaning the people of this world who are immoral, or the greedy and swindlers, or idolaters. In that case you would have to leave this world. 11 But now I am writing to you that you must not associate with anyone who claims to be a brother or sister[c] but is sexually immoral or greedy, an idolater or slanderer, a drunkard or swindler. Do not even eat with such people.

12 What business is it of mine to judge those outside the church? Are you not to judge those inside? 13 God will judge those outside. “Expel the wicked person from among you.”

I picked this one on purpose. Interestingly enough, when you're reviewing the lifestyle or actions of people outside the faith, you are, in a manner of speaking making a "judgement call" without "passing judgement" (of condemnation which is reserved for Christ Himself). Your judgement call is merely a means of determining the kind of person you're dealing with.

Please notice that IF a person is calling himself or herself a 'Christian', it is then that we ARE to determine whether or not that person is truly a follower of Christ and take action if he or she is not.

You do realize volumes have been written on this topic alone and there is no way that I can give an answer that will be acceptable to most people. Good luck... hope this kind-a helps.