Yep -- either the hairs themselves can trigger it, or they have chemicals on them that induce the allergic response. I know an entomologist who handled a dead T. blondi that had been soaking in alcohol and he had a rash that lasted for several days.
So pretty much any new-world T will do this to you. The best bet is to have them only as "display" specimens and not for handling. For tank maintenance, maybe you can have a friend who's not an arachnophobe help you out?