Interesting. Metalangel and I had a course this semester called "Becoming an Ally", taught by an interpreter, and one of the points she emphasized with us was dressing appropriately. As a matter of fact, it was part of our presentation mark. She also recounted a couple of occasions where she had turned up without confirming the kind of assignment ahead of time, and felt she hadn't dressed appropriately for the situation.
For the Interpreting students at our college, particularly the final year ones, they are expected to dress professionally every day. Preparation for the real world, I suppose.