My cousin is a sign language interpreter and he says a big problem he and his clients have is that people talk to him rather than the client. Even at really important things like doctor appointments, the doctor will spend ages asking my cousin where he learned BSL while the Deaf client just wants to get their medical issue looked at. It's against policy for my cousin to hold their own conversation with the doctor when he's working, as he's only there to help the client understand what people are saying.
He and his clients find it really frustrating and rude, so basically if you see someone with a sign language interpreter you can literally just ignore the interpreter and everyone will prefer it that way, as they can just get on with their job!
Also one of his first ever clients saw his doctor was Indian and signed "where's my curry". That was pretty fucking awkward, especially when the doctor then asked what the sign meant.