Call it (pun intended) a smell test. I have cited a study that shows biomarkers of gut inflammation strongly correlated with glyphosate exposure. Perhaps you should have read it.
I have raised a flag. Lowering your exposure to a novel chemical agent that directly impacts a massive and poorly-understood symbiotic system within the body isn't a bad response. Glyphosate exposure certainly isn't beneficial, so I'll treat it like Pascal's wager: avoiding this has more upside than downside.
Maybe you should see if you adjust to the bran flakes, cut them out if you don't improve, and see if there's a difference? All sorts of things can disrupt gut biomes, and I think ancestral diets are an interesting area of study. Gut inflammation is absolutely rampant.
I'm not trying to make a complete argument, I'm trying to raise a flag. This issue is not well-studied and has very large corporate sponsors who would like to keep selling Roundup-Ready™ crops. One particular measurable function is inhibition of the shikamate pathway in many different bacteria (the majority of the volume of your gut flora is affected).
I understand that this is the realm of crunchy weirdos, but thinking holistically doesn't mean you need to lobotomize yourself.
Here's another paper examining some brain effects of chronic gut inflammation, which could be reasonably inferred as a potential consequence of long-term glyphosate exposure: https://pmc.ncbi.nlm.nih.gov/articles/PMC10661239/
Well, I didn't intend that as a conversation-ender, but it is true. This particular substance inhibits a particular function of certain gut flora that seems important. I think it's safe to call that significant.
Here's a decent one: 13% of the UK reports gluten intolerance symptoms, and only 7% of Germany does. The UK allows pre-harvest glyphosate desiccation, Germany doesn't. I would be happy to bet that the trend continues past my quick Google search.
The mechanism of action of glyphosate inhibits several important amino acid production processes in the gut. I'm simplifying here, but not having glyphosate in the food supply would be a good thing for the gut, and the science agrees on this.
Glyphosate for field prep also doesn't really come through in food, it's much worse with the pre-harvest desiccation.
The best-reasoned criticism of glyphosate is that it disrupts the gut biome (this is a fact). I suspect that many "gluten allergies" are actually gut biome problems from glyphosate-desiccated wheat.