I think because it seems.... very arbitrary, and many people (not necessarily you) are very judgmental with their bias.
To me, you being biased against a person with a tattoo seems no different than you being biased against a person for owning a pickup truck, or for liking Harry Potter, or for playing WoW. Generally speaking, the fact that a person has a tattoo means nothing except that they have a tattoo.
(I am distinguishing here between a bias against a person with any tattoo, compared to a bias a person has against someone that has a particular tattoo they find offensive.)