Answer: Nothing I've read about dodder indicates that there should be any problem eating plants it has parasitized. The New York Botanical Garden Illustrated Encyclopedia of Horticulture states, "The gardener's only concern with dodder is to eliminate it."
So you should be fine eating the herbs, just avoid ingesting plant parts that have been parasitized. Most importantly, I'd begin doing what you can to eliminate the dodder now. This will include pulling out affected annual plants, and cutting back perennial plants, if this is possible. Destroy the dodder before it sets seed, because this seed can lay dormant for several years, ready to reinfest. (Dodder flowers are tiny, yellow or white, and occur in clusters along the stems.)
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