That part within the Navajo Rez is the Hopi Rez. All dry.
You have to go to a border town like Flagstaff, Gallup NM, or Farmington NM for booze.
For a friend, I was trying to get beer on a Sunday in Gallup, which was even harder. I had to ask a few people and finally got directed to a bar up a hill. It was closed (Sunday AM), but I went around back and they were selling cases for cash only.
You know. Cuz Jesus.