I have no dog in this fight, i am simply a 4th year applying to pediatrics so I probably shouldn't even chime in. But as someone who has full sleeves, I am aware that some people want their doctor to look the part and not have tattoos, but for every one of those patients there is another that wants a physician who is down to earth and able to connect with them. Anecdotal evidence, but I have had patients tell me that knowing i have tattoos makes them feel more comfortable. I enjoy tattoos in the same way one may enjoy art. Some art they hate, some they love, and some they are indifferent. I am aware people will judge me because of it, but being more accessible to patients is something that many millennials are looking for in a doctor. And in my mind, life is too short to be concerned with who is going to be put off by tattoos. I didn't get them for other people.
Full disclosure, i do keep them covered almost all the time, and I am aware most people have enough tact to not tell me their thoughts on tattoos. And maybe I chose peds because many of the parents i deal with a millennials. Anyway, have fun.