This is an appealing myth, because it fits nicely with popular conceptions about giant agro-businesses and their insidious role in ruining our health with high fructose corn syrup and genetically modified Frankenfood. There has been an increase in the incidence of celiac disease in the second half of the 20th century. And wheat that's been genetically pumped up with extra gluten would provide a nice simple explanation for that phenomenon.
Inconveniently for gluten conspiracy theories, though, in a study published in the Journal of Agricultural Food Chemistry in 2013, researcher Donald D. Kasarda analyzed data about wheat breeding, and found no evidence that wheat contains more protein than before. Additionally, Kasarda noted that there isn't any GMO wheat used commercially in the U.S., so gluten content isn't being increased that way, either.