It is important that you know what your paints are made from, and you should always work in a well ventilated space.
Your safest best, however, is to think of all of your paints and mediums as potentially harmful, and to treat them equally. Paints labelled non-toxic are considered safe for humans, but are not necessarily safe for the environment. Propylene glycol, for example, is safe enough for use in the food and cosmetic industry, but has a disastrous effect in aquatic environments, meaning that pouring acrylic waste water down the drain is damaging to waterways.
Oil paints are essentially made of two components: pigments and a vehicle; acrylic paints are composed of pigments, plus a vehicle and a binder. Vehicles are the liquid part of the paint that holds the pigments in suspension, and binders act like cement, allowing the pigments to stick together and form a paint film.
In oil paints, the vehicle and binder are one and the same: highly refined vegetable oils such as flax (which the paint world calls “linseed”), safflower, poppy, and walnut. These oils dry slowly through oxidation, creating a hard film of paint when they come in contact with air. A skin forms over the paint surface, while the paint underneath continues to harden over time. Used alone, oil paints don’t release any chemicals into the air as they dry. But, if you’ve added solvents or mediums containing petroleum distillate to them during the painting process, their harmful contents will evaporate into your studio space.
Acrylic paints contain the same pigments as oils, but their vehicle is acrylic polymer emulsion, and their binder is acrylic polymer. When they dry, the components of the vehicle evaporate—meaning that water, propylene glycol, and ammonia are released into the air. Some of the commonly added acrylic mediums also release formaldehyde as they dry.