Note: Realistic enough
The short answer is, it depends. Early on it can be extremely unrealistic. Think a sketch on a piece of paper. This just helps you rule out early the ideas that just don't gel.
As time goes on, up the fidelity, move on to slightly more realistic prototypes as you are feeling more confident about the direction you are going in.
Sometimes you might find that a very unrealistic prototype will not yield accurate results and that you may have a 'hunch' that it might work better in reality. I would say, test that out. Don't just abandon ideas that you feel confident about based on small sets of user feedback. There are times where the user simply isn't used to a new concept and where it might take a period of "educating the market" to change consumer confidence. An example is AirBnb where there was intitially a barrier to overcome with staying in a strangers house. But, as with AirBnb, it may mean you need to find the right user group that will cherish your idea early on. If you have a small, passionate, customer following, you'll be able to build an incredibly successful service or product.