Agreed in the bad taste/old fuddy duddy
Take your pic really.
I had a similar argument with a company director who was adamant that anyone of 'consultant' or above grade (IT, not medical) must look the part even down to the hanky in ones pocket. Yep he wanted me to force this kind of dress code on the guys working in my team, whereas I'd rather judge people on their ability. Of course I wouldn't recommend anyone get a tattoo of something obscene on their forehead or prison tattoos on their necks, but otherwise see no problem.
And yes for the record I have a couple of tattoos myself that cannot be seen under sleeves etc and once had a wonderful conversation about the [lack of] intelligence of people who choose to do this to themselves. The guy even went on to say "funny...you seem brighter than that" after finding out I have them myself.