Being non judgemental and respecting the fact that someone else may have an opinion which differs from yours ...even although you secretly know that they are completely delusional!!!!!???

To me it means listening to a person's argument and engaging with them in dialogue.

I think it means being aware of what you think, and especially about what you 'believe', and being willing to challenge those beliefs any time new information comes to light...

That the speaker has self delusions of grandeur. They can’t be bothered to consider the issue but are too self conscious to admit it.
They don’t understand the issue and too self absorbed to ask more about it

One of the great quotes from Princess Bride, "You keep using that word. I do not think it means what you think it means." While the rest of us can probably agree that it means able to delay judgment until all the facts are in, there are also those who will likely inaccurately describe themselves as such, in much the same way as some say they have a sense of humor or can take bad news when experience and history indicate otherwise.

It should express a willingness to discuss the idea.

If you're referring to arts/entertainment I agree whole-heartedly. For any other venue, I have the knee jerk reaction of 'just what is it you're trying to sell?'. Most other times I've encountered this or a similar statement it's being used as a defense after facts contradicting an assertion are presented.

The ability to entertain an opposing viewpoint.

"To always remain willing to reevaluate what you believe, no matter how certain you feel about it."