If you have bare hands when you cut up an animal, you have to wash your hands before you eat/drink. If you are wearing gloves, it doesn't matter. You don't need to wash your hands. But why would you be able to eat/drink while wearing the gloves with zero chance of getting sick? I would say the gloves become contaminated, but you can take your gloves off and eat/drink and you'll be just fine, but if you eat or drink with the contaminated gloves on, you'll have a chance of getting sick from that.