First thing is to never wear a stupid white shirt to an REO. Jeans, old shoes, long sleeve older shirt. Inspecting an REO is not the time to try and impress the bankers. And besides, everybody knows that white shirts attract most bugs like fleas and ticks.
Given some of the places I've been in my life, here and over seas, I seriously doubt there is that much to be fearful of during a brief visit to an REO. I do get a reaction to certain mold but just about everybody does. It is not going to kill you. (No such thing as "toxic mold")
So dress the part, move as little as possible in gathering data, take thousands of pictures and get out of Dodge if this kind of thing bothers you. If it really bothers you, don't accept any more REO assignments.
I didn't know that about white shirts. However, I never wear a white shirt anymore except to funerals.
Actually, I think I have done as many "unhealthy" privately owned and owner occupied homes that were in gawd awful condition as I have REOs. Sanitary wipes are a very good idea even after visiting a clean looking home. I have been to two drug stores and KMart looking for them. I have found "wet wipes" as well as those with chlorine bleach in them for use in cleaning sinks and other things, But, no "sanitary wipes." I did not feel the Clorox infused wipes would be good for my tender and dainty skin (or eyes).