I am covered in visible tattoos: I have a full sleeve to the wrist of my right arm, and a half sleeve on my left arm. These are no trouble in clinic or hospitalist rotations as you can just wear a white coat and/or dress shirt. The trouble I did have was in the OR when they were visible. I had even been "reported" by one of the staff in a rotation I thought I was well liked (my mistake) - nothing came of this though.
Medicine, which has on the surface quickly become a super liberal overly-PC field where you are considered horribly offensive if you don't recognize things like alternative genders, is still deep down stupidly conservative. There are a set of rules for your image: dress shirt, tie, white coat, polished shoes, short hair, no piercings, no tattoos. Does it matter that ties and white coats are filthy fomites and are proven to increase infections in hospital? Nope. Does it matter that you can do your job just as effectively in blue jeans (as many do in europe)? Nope. Is it sexist that women can have long hair and piercings but men can't? Maybe. It sure is ironic in a field that is supposedly so liberal and outwardly inclusive.
There are reasonable, progressive people in medicine and there are old school types who thinks anybody who doesn't fit the above image is a dirty hippie and on "the drugs." The former, by their nature, don't give a sh|t about what you do and won't cause you any trouble. Whereas the latter will go out of their way to try to eliminate people who are "different" because they are insecure little men. I recently watched an attending observe a foreign student wearing blue jeans with a white coat. The person in question was probably 50 ft. away, but the guy caught it out of the corner of his eye, watched intently for about 5 minutes (it took me a while to realize what the hell had caught this guy's attention and that he wasn't seizing), and then over the next hour or so, pull about 5 different people aside to whisper and gossip about it. I observed the same thing a year prior where apparently emails had been sent out in another department and the entire staff was gossiping about it so that the daily convo was whether the "blue jean talk" had occurred yet. It blew my mind that it was that big of a deal. Because when it comes down to it, they are goddammed cotton blue pants with a unique pattern. That's it. Non-patterned blue cotton pants are allowed.
Anyway, the entire point of all this silliness is that we follow these rules for the same reason the pilots who step on your airplane are wearing funny uniforms with a big hat and wings and stripes on their jacket. It engenders trust in the hundreds of souls who are putting their lives in their hands. The reason American Airlines doesn't let their pilots bust into the plane wearing flip flops, cargo pants, and giant holes in their ears is largely the same reason doctors get warned to lose the long hair, cover the tattoos, and not be seen carrying around a motorcycle helmet.