It’s a sad reflection of our times that people are so judgemental, and look at the tattoos rather than the person -but that is the way it is.
The view I take is that you will only change those peoples attitudes one step at a time. Show them that despite the fact you have tattoos, you take your job seriously, you do it well and in a professional manner.
They soon stop seeing the tattoos and start seeing the person. Next time they see someone with tattoos, they are not so quick to leap to conclusions.
As far as employers are concerned, they are paying your wages, and they need to feel that they are getting value. If they think their customers are going to shy away from you because you have a tattoo, they won’t feel that they are getting value for their investment….. not necessarily fair but it is how people see it.