My opinion, I like the color!

If I went with a color, as I might be tempted to do, I'd select a shade or two darker than the color it is now. If that's not an option, I'd be tempted to select a neutral color out of your stone and paint the breadboard that color. I DEFINITELY would not put a color in that very neutral kitchen!

If you put a color behind the shelves that contrasts with what you have displayed on them, you risk having a very cluttered feeling in this room. Right now, your tile backsplash has a nice subtle pattern and the counter top stands out a little stronger. Another strong pattern would minimize the tile pattern. If you leave the walls white or neutral, you still have the ability to make a pop of color with a decorative piece displayed on the shelf.

What your open shelves need is colored dishes so that they stand out against the wall. The dishes you have are lost against the wall color which is why I would consider a darker wall color or new dishes. I'd like some color in the dishes, even if it's just a few of them.

I would paint the shelves and the wall behind them the same color as your island.

I agree with the idea of colored dishes to make that area pop. I like the white tile you have behind the shelves right now, but without even a smidge of color it can look really sterile. I have all white dishes and have recently picked up some colored serving bowls from HomeGoods...I love that they add a bit of whimsy and life to my table and I can change up colors as the mood suits me but I don't have to buy a whole new set of dinnerware.

Totally agree with everyone else that your dishes blend in with the wall color. If you love the dinnerware then just add to them. Choose a color used in your home for accent pieces such as bowls, decorative vases or jars. You can also breakup the white with some copper or stainless steal cookware. One other bit of advice. I think matching your island to either the upper or lower cabinets would bring everything together. The white looks unfinished.

Good observation from Gina...the island color is rather stark against the rest of the kitchen, tho it might be just the photo, and not that way in person. But consider toning the white down to a color from the granite countertop.

You could add a band of tile like in your backsplash on top of the beadboard to finish it off...it would change the whole look of that wall.