Speaking from the student-side, I can assure you that several of my professors have tattoos. That being said, they seem to try to make them non-visible, or in locations that can be hidden via professional clothing. I'm not sure that it's necessarily for prejudicial reasons, but it is a deep-set concern for a conservative idea of professionalism, which is a fact if you mean to teach in some American institutions. However, I think that depends on the institution. I definitely know several colleagues (also students), who have full sleeves, several ABD or in the final stages of PhD. (They often wear long-sleeves, on work days.) So...You know, it will vary, but being able to cover your tattoos will likely make you more versatile for the market, depending on the conservatism of the institution.