Its called galvanic corrosion. You need an electrolyte (water, acid, etc) and oxygen (can be in the electrolyte) for it occur. Being that the racks are not exposed to constant water, kept in an environment around 30% humidity it will be decades before any corrosion will occur in this situation. If it was an issue I could isolate the two or suppress the problem with a low voltage (mV) dc current.
Its the location of the materials on the "Noble" scale shows which will react. Gold being the highest (cathode), Zinc the lowest (anode). The decay will occur on the one with the lower number as the current flows from the less noble to the higher on taking molecules with it. The principle is how a battery works and how we protect all types of metals in harsh environments.