In the early 1980's, I worked in the financial industry where women wore a tailored, skirted suit and blouse. From there I went into nursing; first year was a traditional white uniform; a few years after it was those awful green hospital scrubs. Many people assumed if you wore those green scrubs, you were the doctor. The hospital decided that was too expensive and we switched to whatever scrubs we wanted and purchased ourselves. Some departments did require their staff wear a certain color (blue for respiratory therapy, brown for ICU, etc.) Yes, people treated me differently.
I think part of the reason for that different treatment was the manner in which I presented myself; the language, the words and the way you say them is completely different. A financial adviser will shake your hand when you meet and will assess a client's status by their dress. A nurse will not and doesn't care how you appear as long as you appear relatively clean.
In addition, I was 45 years old when I started nursing; patients and their families displayed more confidence in me because they assumed I had many years of experience. When they would ask me, "How long have you been a nurse?", I would say, "Oh, a while now."