Coffee and tap water reaction - results in gray tint I use filtered water to make my coffee.

If I mix a few drops of said coffee with our tap water, it turns a grayish color; it's much darker than the coffee would turn the water by itself (I compared by doing a side by side comparison and adding an equal amount of coffee to filtered water, resulting in a much lighter brown (not gray) color that is closer to what I'd expect from coffee). It's a very pronounced effect (i.e. easily visible when you rinse out a coffee mug that has just a few drops of coffee at the bottom). Because of the distinct color change and the fact that it's significantly darker than it should be from simple mixing, it's obviously a chemical reaction.

What common tap water contaminants would react with coffee in this manner? Iron perhaps?
The tap water might be slightly hard.  Hard water has a high content of minerals such as calcium or magnesium which makes the water more alkaline. Alkaline water will draw tannin out of the coffee much quicker than pure water.

Filtering the water with something like activated carbon filter then an ion exchange filter will lower the mineral content, thus lowering the pH. With a lower pH the dissolution of tannin will be slower.

Slowing the dissolution of tannin relative to more soluble portions like caffeine is part of the reason for steeping tea and coffee for only a limited amount of time.  More steep time, or more alkalinity in the steeping solution,  releases more tannin.  More tannin makes the coffee more anti-nutritional, more bitter, and it darkens the color.