The main reason why some artists become sensitive to oil painting, is not because of the paint but because of the toxicity of traditional mediums. Oil paints are relatively non-hazardous in themselves. Unless you eat them or let them come into contact with your skin.
Traditional mediums evaporate very fast releasing toxic vapors which cause health problems. Aromatic solvents like gum or mineral turpentine will affect your health with years of regular use because you cannot escape the fumes. Using toxic solvents and mediums in public shared spaces is like passive smoking. Ultimately it is best to avoid these types of solvents.
Though if you still need to use solvents, odourless mediums and solvents are based on fast drying alkyd resins which out perform ‘traditional’ mediums and are better for health. They evaporate much more slowly than turpentines so that less vapour is generated during a painting session. They do, however, evaporate over time, and the problem with odorless solvents is that artists often forget that they are still toxic. Drying racks as well as work spaces still need to be ventilated and painters in lofts should not recirculate the same studio air in living and sleeping areas because a slow vapour build up could become toxic.