Who should wear gloves in the restaurant?

At workplaces that are dealing with food and drinks then gloves are normally worn, to prevent cross-contamination and the spread of illnesses. You don't have to wear gloves with every food you touch but its better to use some sort of a glove whenever you can.

The use of gloves does not replace proper hand hygiene. Sometimes gloves are reused to the extent that they are more dangerous than properly washed and sanitized bare hands.

Remember to wash and sanitize hands before putting on the gloves. If they are the disposable type, replace them often. If they are multi-use gloves, they need to be cleaned and sanitized frequently. The primary purpose of the gloves is to protect the food, not to protect your hands.