Good info, I read those too. The only clear research was with soy isoflavones, not gluten, and there were very small amounts at that.Here is another. http://www.glutenfreegigi.com/what-science-says-about-gluten-protein-in-eggs/
Basically in general the consensus is the proteins cannot pass into eggs but there is high chance of contamination.
Eggs themselves are also an allergen.
But the research is unclear.
That's the summary.