Nickel is the most common metal that bothers people. Copper wire does not contain more than trace amounts of nickel. Please see the metal allergies section of
http://www.rings-things.com/METALS.HTM for more details.
Copper earrings can be worn by many people, however, it may discolor their ear or turn green from the reaction of the copper with body acids. (This is the same reaction that people look for when they wear copper bracelets to help arthritis.) Every body is so different. Some can only wear silver, some only gold, some people can wear any sort of ear wire while others are bothered by any metal in their ear. Just tell your customers that the earwires are solid copper.
Does that help answer your concern?