I can see that this issue is hitting some hot triggers and thought I would try to provide some information. "Organic" is a very broad term. The USDA has an entire training section called "Organic 101" to explain what in included. On the third installment of this training,
https://www.usda.gov/media/blog/2012/03/22/organic-101-what-usda-organic-label-means Within this installment is what seems to me to be a very pertinent paragraph
"When it comes to processed, multi-ingredient foods, the USDA organic standards specify additional considerations. Regulations prohibit organically processed foods from containing artificial preservatives, colors, or flavors and require that their ingredients are organic, with some minor exceptions. For example, processed organic foods may contain some approved non-agricultural ingredients, like enzymes in yogurt, pectin in fruit jams, or baking soda in baked goods."
So, what we have here appears to be what is technically correctly called "Organic" when what one needs to actually require is perhaps "100% Natural". The enzyme is a fungal-based product regardless of how it is commercially developed. A possible compromise might be to suggest that a product without the enzyme included be provided for those who wish a more purist version. Or, perhaps folks could just buy hard red wheat or other variety and grind their own flour. It would appear that making a sourdough would take care of leavening if yeast is not wanted. I found this barley flour version that adds significant healthy fiber to your product
https://www.homecookingadventure.com/sourdough-barley-bread/ .
Sorry, but my engineer's brain tries to explore potential alternatives.