At our office Christmas party a few years back, a married man with several children was aggressively affectionate with a female supervisor. My co-workers were disgusted to the point of revulsion.
At the party, my wife made a very good connection with one of the ladies there and led her to the Lord. This lady told my wife that this exuberant couple was not the only couple the people from work were watching. They were all interested in seeing how my wife and I reacted to them as everybody knew that we were very "religious."
Thankfully, we did not shun them or treat them with disdain. We talked and laughed with them, just as we did with everyone else.
"I found this so interesting," this lady told my wife. "That's why I wanted to get to know you better."
To not judge does not mean that one thinks everything is cool--whatever makes a person happy is just fine, regardless of the wretchedness of the behavior. But it does mean that one treats everyone with kindness and dignity, and does not talk unkindly towards others.