I did not get tattoos until after I left the service... partly because of the mission at the time, partly because I didn't want the hassle. None of mine are visible in a short sleeve shirt, people don't need to know I have them unless they'll understand them...
Face, neck hand and head tattoos are an ancient warrior tradition... but our current general society has fallen away from any type of warrior ethos, and these marks of earned honor have been turned into marks of criminality by gangs and prisons... the usurpation of honor marks by the lowest of the low is sad, and those who earned them honorably in battle have to deal with a stigma of that criminality because that's what the media shows...
A stupid order, if not unlawful, still has to be followed, right? Performance, ability, and growth should be the keys to promotions and retention, not body art that does not impinge on the 'face' of the services.