Like it or not, we live in a world where people judge one another on appearances. And naturally some of those people will be in charge of hiring you and advancing your career.
With that in mind, there are several ways that one can stack the deck against one's self. Morbid obesity, poor personal hygiene, vampire costumes, and, yes, visible tattoos can all serve the purpose of closing a door that might otherwise be open to you.
The questions you need to ask yourself are how important is it that all possible doors remain open, and whether you're in a position in life where the occasional closed door leading to an environment you don't want to inhabit might actually be a good thing.
And of course, the big question. Is there even the smallest possibility that several decades from now your life, values, opinions, career, etc. will have evolved to a place where you find it really really inconvenient to have a marker of the social situation and personal biases you happened to have at age 19 permanently stamped onto the back of your neck.
I certainly wouldn't want that guy in charge of my tattoos today.