Is it true that Jehovah's Witnesses shouldn't associate with non-witnesses?

It depends what you mean by 'associate'.

Jehovah's Witnesses do interact with non-Witnesses. In fact we visit non-Witnesses at their homes. We want to help them on a very personal level to draw close to our 'Father-in-common' Jehovah God.

-- It's usually the other way around with your question -- non-Witnesses don't want to associate with Jehovah's Witnesses.Many are actually very rude to us. I've had the door slammed so many times right in my face, without even being given the courtesy of introducing my name. Yet these people CLAIM to be 'Christian'.

But granted it's true:

1. we don't seek too much 'CLOSE' association with people who lie; for example: to their children about Santa bringing their children gifts at Christmas time. (What message would we be sending to our children if we winked as such 'adult-accepted'; 'religion-accepted' lying?)
2. We also don't seek too much 'CLOSE' association with people who worship a god who punishes people with 'eternal torment' in a fiery hell. We think it would hurt Jehovah God, if he saw us hanging around constantly with people who view Him so cruel.
3. We also don't seek too much 'CLOSE' association with people who deny the existence of Jehovah God; and who don't credit him with 'creation'. (Again, what message would that be sending to our children, if we hung around such 'denyers' of God.)

But be it clear - - our not seeking such people as close associates, is not to be confused: that we don't show love or compassion for non-witnesses. Just the opposite -- that's why we're the ones who visit them, and quite regularly at that; even more often than their own pastor, priest, or other clergy person.

We usually seek close association with people with whom we have things in common; I guess like everyone else would.