I was a hiring manager for years and many companies have policy and procedure that lists what is and is not acceptable. In general if a position requires contact with the general public then piercings, not including ear piercings, must be removed or appropriately covered. Tattoos must be covered as well. In some cases the tattoo policy is less strict based on the appropriateness of the tattoo and the location; this is however determined by the manager and specific company.

The issue is that not everyone likes tattoos or piercings. For example, an elderly customer might not want help or to even associate with someone with visible piercings or numerous tattoos. Most restaurants are the same, that's why you'll notice servers with wraps on their arms. They are hiding their tattoos. One of my good friends puts a band-aid over her nose ring every day when she goes to work.

It's just the way it is. There are plenty of positions that are less strict on dress and appearance codes, but you have to find them and often they require more advanced degrees, such as office / research / field positions. Other places have been mentioned such as "trendy" merchandisers that are more than happy to allow piercings and tattoos.