The most allergenic fragrances are natural.
In a study of natural cosmetics from 1996 22 natural perfumes were chemically analysed and 82 percent of the perfumes were found to contain known allergens. Some samples had allergens in such large quantities that they was considered too dangerous to use.
Viewed from an allergy perspective, it is not healthier or less risky to use natural extracts/fragrances rather than synthetic perfumes.