It would also depend on what sort of job, clearly.
Say it was a nanny - absolutely would not hire them with visible tattoos, piercings or outrageous hair. But then neither I would not hire someone who had an obvious accent or any speech impediments as my children are young and one of them needs assistance in that area. At the same time I probably wouldn't hire a vegetarian because I would like the nanny to eat with the children, and to prepare meals that include meat. I would prefer to avoid hiring a strong atheist, or someone with strong religious beliefs that weren't Christian, and I wouldn't hire a fundamental Christian either - someone with laid back beliefs would be fine though.
In other words, the nanny would be chosen to fit in with us, our lifestyle, and our beliefs. But that is because of the time they would spend with my children, in my home.
Someone hired to design and run my internet page, couldn't care what they looked like. They could have tattoos, piercings AND brightly coloured hair and I wouldn't bat an eye.
Personal assistant for my DH, who needs to meet and greet influential people, no visible tattoos, visible piercings, bright coloured hair, accents etc wouldn't phase me as long as they didn't interfere with the job.
Person colouring my hair - would choose someone with the sort of look I like. Mistakenly went to a salon once where all the staff had the super blonde hair, and my highlights ended up the same shade of super blonde even though I specifically asked for golden blonde, that was far darker than theirs. Felt like a misplaced surfer for months....
So you see it all depends on what sort of position I am looking for someone for.