However, when people use the "do not judge" argument, they are saying that you should not question or debate lifestyle choices, actions, or alternative beliefs in any way. I counter that this use of this "judge not" command is out of context and does not mean that Christians (or anyone for that manner) should not use their judgment. Taken to the extreme, our society would rapidly disintegrate into chaos.
Yes, we should not be pious, "holier-than-thou", or to ever consider ourselves better than others (because we are not). "Do nothing out of selfish ambition or vain conceit, but in humility consider others better than yourselves." (Phillipians 2:3) Conversations should be in love with the best interest of others as the primary objective always. (Matthew 22:36-40)
I found this article today on "Judging Others" to be a very good synopsis:
"Judge not, that ye be not judged." (Matthew 7:1)
On the other hand, this caution by no means relieves us of the responsibility of evaluation the beliefs and practices of others in the light of Scripture. In the very same sermon, in fact Jesus said just a few moments later: "Give not that which is holy unto the dogs, neither cast ye your pearls before swine"; and, "beware of false prophets, which come to you in sheep's clothing" (Matthew 7:6-15). Obedience to such commandments obviously requires one to make a judgment as to whether certain unbelievers should be regarded as "dogs" or "swine," to whom it would be counterproductvie to try to speak of spiritual matters; or whether certain profession Christian leaders [ed. should this be limited to only "Christian leaders?] be limited to are actually false prophets who should be repudiated. Jesus also said: 'judge not according to the appearance, but judge righteous judgment' (John 7:24)
Since the Scriptures themselves are to be used in the final judgment (John 12:48; Revelation 20:12, etc.), it is obvious that we should use them right now to discern truth and error, right and wrong. 'For the word of God...is a discerner of the thoughts and intents of the heart.' (Hebrews 4:12).
There is another basis of judgment that the Lord Jesus has authorized us to use. 'A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit....Wherefore by their fruits ye shall know them.' (Matthew 7:18-20). Thus, by the test of Scripture plus fruit produced, can serve as the basis of a valid judgment. Until adequate data for making such a test are available, judge not!"
Morris, Henry H. Ph.D., "Judging Others", Days of Praise; Institute for Creation Research, 2008.