DOPs would be easily tasted if they were gassing out - you may melt the plastic though. Microwave oven excite the water molecules. In certain cases you can have localized heat that is way above the glass transition temp or even the melting point of various plastics - heck it some instances it could exceed the decomposition temp then you would have some issues.
I wouldn't worry so much about the plastisizers as I would the decomp product of the various polymers. Years ago (in grad school) we carried out many polymerizations and de-polymerizations in aqueous phase using microwaves. There has been a ton of study in this field.
http://www.schubert-group.de/publications/PDF/Papers/Wiesbrock2004_1.pdf
ScienceDirect - Polymer : Rapid microwave induced depolymerization of polyamide-6