Standard medical latex gloves (or some other type of medical grade protective gloves) should always be used. Another point worth mentioning, though: Do the gloves fit properly? If the gloves are too big or too small, the artist runs the risk of either poking a hole in the gloves or tearing them. All it takes is a pinhole to run the risk of cross contamination.
Granted, this is more for the safety of the tattoo artist, but no one wants an infected tattoo artist working on them. If the tattooist doesn’t care about their own safety, why would they care about yours?