FYI, don't know about other branches of service but the Navy now restricts visible tatoo's. If you had one before the change you're grandfathered in. If you apply with one, you need a waiver. If you want a new one it takes an approval process I know nothing about.
I know for a fact we admin seperated a kid in my last command for going out and getting a new sleeve, knowing full well the policy was in effect.
Not in anyway anti tat, I have one myself, but as others have said it's all about what the customer thinks when they see you up front.