Do tattoos really matter when working with animals?

I have decided that I am going to finally do something I love and work with animals. I have been looking into “this program” http://mcweb.moorparkcollege.edu/~eatm/ and a few others. The thing is that these programs say that visible tattoos are not allowed and are generally not accepted in the animal field. WTF?

Is this true? If you work with animals do you notice that people are not allowed to have tattoos? What is the reasoning behind this?

Every vet I have ever gone to seem to let people have tattoos. Why is it different when working with non-domesticated animals?

Are my tattoos going to hinder my employment prospects?