Is spray foam insulation toxic to people?

Spray foam insulation manufacturers advertise it as a non-toxic material, and that only those installing it need to wear any sort of protection, because when it dries it is not supposed to be dangerous anymore. It contains no formaldehyde, like some problem insulations. However, it is made using what is called diisocyanates, which have been implemented in causing asthma, and are a well known toxic substance that some people are sensitive to. They can cause nerve issues or other illnesses. It is recommended that protection be worn by workers, and that all those who live in a home where it is being installed need to leave, until all the fumes are gone, all the foam particles swept up and everything cleaned.