Do I need special gloves for mozzarella stretching?
There is no requirement for specific gloves so far as I know. Gloves themselves aren't actually even necessary. They do however keep your hands clean, and they keep any nasties that could be on your hands or arms out of the cheese. When I make mozz for my family I usually just use my clean bare hands. If I was making to sell I'd most likely use food service gloves with a little butter on them to prevent sticking during stretching, similar to when you're pulling taffy.