Which tools should not be operated while wearing gloves?
from OSHA Guide for Protecting Workers from Woodworking Hazards

Hand and Arm Protection

Your workers' hands and arms will need protection from burns, bruises, abrasions, cuts, and exposure to the chemicals used in finishing.

Protective gloves are the primary means available for direct hand protection. Extra-long gauntlets or sleeves attached to the gloves can extend protection up the arm. However, the appropriateness of glove use in the woodworking workplace should be carefully reviewed on a task-by-task basis. Gloves should not be worn when operating woodworking equipment due to the potential for getting caught in moving parts.