Those who are steeped in the sins of the modern era (which are usually sins of the flesh, or directly related to it, such as abortion and invalid "marriage") whip out this passage as a way to console themselves in their sin, or to try and deflect criticism of their lifestyles.
They say "not to judge", but if you could ask the person (a) "are you aware that this is a mortally sinful act?", and (b) "do you fully want to do it?", it would be pretty hard for them to deny being in mortal sin. The sin of contraception, for instance, requires a trip to the drugstore and/or a consultation with a physician, and nobody commits such an act on the spur of the moment (coitus interruptus possibly excepted) in paroxysms of passion or with clouded intellect. Similarly, invalid marriage requires a visit to the courthouse for a marriage license, and seeking out an officiant. Full consent of the will has to be presumed.
"Judge not, lest you be judged" is a Scripture verse that everyone knows by heart, and much-beloved by those who want to live in sin and not be called out for it.