People think this for the same reasons you think someone with baggy pants who likes wrestling may not be good at helping someone in a library.
It's a stereotype, especially among older generations, that people with colorful hair and piercings are rebellious/dont follow the rules. They think we are very uneducated and probably dropped out of school or got the worst grades so they dont trust that we will give the best care. It is also deemed to be "unprofessional" to have different colored hair. Although if you have a deep burgundy that's almost brown you can get away with it or platinum hair that is borderline silver.
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Another thing that makes me cringe is someone not washing their hands after using the bathroom or after they touch raw meat