Actually no they can’t
If it were just up to me, they could.
When I was in the USMC, people could have tattoos as long as they weren’t visible when in uniform. No face, neck, or hands tattoos were allowed, but it was rarely enforced. Guys got tattoos all the time with their wife or girlfriend’s name, or the USMC logo. My daughter’s friend from HS went into the USMC, and eventually became a Drill Instructor at Parris Island. He had the Marine Corps Emblem tattooed all across his chest, from shoulder to shoulder.......................