Mike, very good question, here is a link to a toxicity chart, many of the woods commonly used for making calls are on the list.
http://www.wood-database.com/wood-articles/wood-allergies-and-toxicity/For basic shop safety covering exposed skin with some kind of barrier cream can help. I usually wear a long sleeve t-shirt (or turtleneck) while turning to keep most of the dust off bare skin, facemask and respirators are also good basic safety measures as well as dust collection systems and air filtration. It is the tiny dust particles 2 microns or smaller which are the most dangerous.
Ocasionally, I read of someone having a reaction to drawing on a trumpet made from wood in the Dalbergia (rosewood)family, however calls have been made from these woods for years. Be sure to thouroughly blow any call out before drawing or blowing on it, with compressed air. (Backpressure can send the particles into your lungs instead of out of the call). I seal the internals with mineral oil applied with a pipe cleaner which seems to help,odorless, tasteless, and non toxic, (not sure what other callmmakers use for sealing their internals.)
Symptoms usually present in terms of eye irritation, itchy skin, hoarsness or irritated throat, cough, feeling as though one is coming down with a cold, at least in my experience. When symptons present, it is a good idea to back off. Once you begin to develop a sensitivity to certain woods, it seems sensitivities will develop to other woods as well. (I have my own list of woods I prefer not to work with!)
As long as the call is dust free, sealed and sanitized, it should not pose a health risk to your customer unless he/she is very sensitive to the materials used, the call maker is at the most risk in my opinion.