I'm confused. Your post sounds like you're saying you grow using the bales instead of earth. I've seen raised beds using straw as ground cover. If the latter is what you're asking about I suggest that the straw will not affect your produce. The vegetables get their nutrients from the soil.
composting transforms the straw into a different product by breaking it down into a more complex product to enrich the soil. When you consider that most vegetables never have gluten, I suggest that the ones that you plant will have the same nutrients no matter how they are grown.
That means that the nutrients within naturally gluten free or low in gluten will remain gluten free or low in gluten. Plants grow by a plan embedded within the seed. Straw.is a natural plant.
Perhaps you are relating the process in which plants grown using pesticides are believed by some to include pesticides. Pesticides are not natural. Straw, unless of course grown with the use of pesticides, is natural.
The science of how to grow food pesticide free is new. We are still learning.
Straw contains few nutrients.It doesn't contain gluten. It is fed to animals to provide roughage. It is used in gardening as mulch. I doubt one can successfully grow vegetables.