First, you need to make a distinction for epoxies intended for an industrial environment. There are some kinds of epoxy, and some handling methods (like spraying epoxy for finishes), that are hazardous and need a respirator and skin protection. Epoxy sold for home use is much safer, and products sold as art supplies are covered by regulations that require them to be pretty safe, including being non-toxic, at least when used as directed (ingesting the stuff can be harmful).
There's mainly two kinds of exposure to protect yourself against.
- Skin contact. The epoxy components can irritate your skin. People can even develop allergies to it. Solvents you might use to clean it off your skin can be more harmful than the epoxy, itself. It's generally a good idea to protect your skin from accidental contact by wearing gloves. It can be hard to get out of clothing, and the components remain a sticky liquid for a very long time (which can lead to skin contact), so protecting your clothing is common sense. It's also common sense to wear some form of eye protection. There may not be much chance of getting a splash in your eye; but if you did that would really ruin your day.
Respiration. Epoxy doesn't generate much in the way of fumes, and the fumes aren't labeled as poisonous (a technical distinction, see footnote1). Using small amounts in a well ventilated place is safe, and you generally don't need a respirator to occasionally make some small castings.
But concentrated fumes can irritate your respiratory system, and repeated exposure can cause chronic problems. If you make huge castings, work in a small space with little air circulation, use epoxy frequently, or have a compulsion to get your face close to the components or the uncured casting to continually inspect things, it's better to use a proper respirator (one designed for fumes, not a dust mask). It's a matter of how much excessive exposure and how often. People also vary in their sensitivity. Someone with a chronic condition like hay fever may already have inflammation and be much more sensitive to the fumes.
If you generate fine dust, especially from freshly cured epoxy, which might not be 100% reacted, like by sanding it, you should wear a respirator, or at least a good dust mask. If you get those fine particles in your lungs, they can be harmful.
West System, an epoxy manufacturer, has a really good safety guide available as a PDF link: West System Epoxy Safety. They also have a great broader discussion here: Epoxy Safety - Using WEST SYSTEM Epoxy safely.
1 Note that "poisonous" is a technical distinction related to the nature of potential harm. "Poisonous" seems to be reserved for materials that cause harm by chemically reacting with your body rather than materials that cause physical irritation or interference at the area of contact (which could potentially still result in your body producing harmful changes). "Non-poisonous" doesn't necessarily mean not potentially harmful.
