I don't think there are many employers in our industry who will claim they will "only hire pilots covered in tattoos".
Other way round - quite probably. It might be all fine and happily accepted in one area of the world, but we are in a global society now, like it or not, and not all cultures are so keen on seeing a "painted warrior" in the front of the cab. We are not an industry than generally encourages large degrees of self-expression in our work, it tends to have certain safety implications.