I always like to joke that it would be easier for me to get a web designer job if I had sleeve tats. The truth behind the joke is most young designer types do seem to have them.
I think it depends on the company and the content and location of the tattoo.
Some companies are old-fashioned and won't hire you. Others may put you to the front of the list because you look hip. Most fall in-between these.
Facial or neck tats tend to be associated with criminal activity thus have a more negative connotation to most people. Of course, tats with racist, political statements or other provocative themes or language will also be a problem.
Funny you say that. Every UX person that I've worked with that's been great has had great tattoos, so I definitely fall into this explicit bias.
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