"Ancient Greeks and Romans often used tattooing to mark someone as either a criminal or part of a specific religious order or cult." I'd say that's where you problems of image began.
I'd say today, tattoos are much more mainstream. That's okay. But they are a sign of some other "unknown." Advising a young man away from getting neck tattoos or tattoos on his hands or face, would be solid career advice regardless of how strongly he feel about getting that tat.
It's not that the untatted of us disrespect your creative drive to ink yourself, but there are very few professional careers where a Harry Potter spell written on your wrist is going to be a "fit." Why put your "mark" on broadcast for all of us to see your "affiliation" with Griffendor?
So, when I see a young woman working at the Apple Store (Congratulations for getting this cool gig.) sporting an enourmous tattoo of her preferred Quiddich team, I'm not repulsed. I'm curious. I have learned to keep my own opinions about tattoos to myself. "None of my business."
But, if you're getting a lot of tattoos there's another process at play. You are choosing to make your mark on your skin, and what and where you get your mark it up to you. AND, know that your neck tattoo, no matter how precious to you, may not be showing your best side to the person who is going to make a decision about hiring you. And that's what your post is about. Why the stigma?
It's not like tattoos have the stigma of a "mental illness" diagnosis, but the cultural judgement is not far behind. Tat up all you want, but know that to us #boomers and #genx folks, it's more about your decision to get a tattoo there more than it is if the ink is Mickey Mouse or Maus.