To 'service' a piece of equipment means to repair it or perform maintenance on it. To 'service' a person means, in common parlance, to gratify sexually.
I have been serviced by several women with tattoos, and I have always been more than comfortable with that; I have been excited.
As for being served in a business by a tattooed person, that is now commonplace in the Us. Over the last 50 years we have become a culture that embraces tattoos, thus joining ranks that include many cultures throughout the Pacific. I know several people who are the third generation in their families to have ink. Once nobody has any reason to worry about what Grandma will think, the behavior is normal in the family .
A decade ago, I taught in a Californian high school. Teachers are a relatively conservative demographic, English teachers especially so. There was only one un-tattooed person in the English department. None of us hid the tattoos; in fact one teacher had full sleeves, and he routinely wore short-sleeve shirts at work, including parent conferences. He never had any complains about his appearance.
To be fair, someone with a swastika tattooed on the forehead is likely to give anyone pause.
A tattoo is a body modification, and it is also a desire. If someone has a tattoo, that means they desired it (or they got really drunk). Who am I to judge human desire? The person's skin and how they represent themselves has nothing to do with their ability and skills. I feel that as long as they can perform the job, they should not be treated any differently from someone without tattoos.