Q:

Do Monsanto GM foods cause gluten-related illnesses?

In a newly released video by RT they claim that "Future Epidemic? Monsanto GM foods cause gluten-related illnesses"
http://www.youtube.com/watch?v=VyV001qX2i4

18 million of Americans suffer from gluten-related illnessess - that's thanks to the genetically modified soya and corn they eat, a survey reveals. Medical experts say it may become an epidemic for the next generation, prompting more and more Americans to choose a gluten free diet. RT's Marina Portnaya investigates the seeds of GMO-phobia.

Clearly stating that it is attributed by consumption of GMO food.
Digging further and finding the article on their site, reveals a different story: "GMOs linked to gluten disorders plaguing 18 million Americans - report"
http://rt.com/usa/gmo-gluten-sensitivity-trigger-343/

Genetically modified foods such as soy and corn may be responsible for a number of gluten-related maladies including intestinal disorders now plaguing 18 million Americans, according to a new report released on Tuesday.

So here are the claims to verify:

Do Monsanto GM foods cause gluten-related illnesses
Can Genetically modified foods such as soy and corn be responsible for a number of gluten-related maladies (and how likely?)

P.S. I know similar topic has been discussed multiple times, but this is specific to Gluten related illnesses and in the light of recently released report. 
Is GM corn toxic?
Is Genetically Modified food safe to consume?

A:

The report this is based on is "Can Genetically Engineered Foods Trigger Gluten Sensitivity?" published by the Institute for responsible technology. As far as I can tell this is not a peer-reviewed scientific paper.
On reading through it, the report makes a lot of small individual claims about the effect of GMOs, or the specific proteins inserted into GMOs like bt-toxin. Each of those claims would deserve a full post here, I'm not going to dissect all of them in this post.
But that is also not necessary, as the report does not actually show any causal link between GMOs and gluten sensitivity. It creates a narrative that implies this link, but in the end it even states that there is no sufficient evidence:

While there is insufficient research to prove that GMO consumption 
  causes gluten sensitivity, the evidence does show how it might, at
  least,  exacerbate the symptoms, or contribute to the conditions that
  might  lead to the development of sensitivity to gluten

This report was also criticized heavily by the Celiac Disease Foundation in this article:

The report, published last week by the Institute for Responsible
  Technology (IRT), was "speculative," Celiac Disease Foundation CEO
  Marilyn Geller told FoodNavigator-USA. 
"There has been no scientific
  evidence put forward for a GMO/celiac disease link that is supported
  by the CDF Medical Advisory Board." 
Meanwhile, plant geneticist Dr.
  Wayne Parrott - professor of crop science at the University of Georgia
  - claimed the report relied on "a handful of deeply flawed" studies and did not reference the "more than 1,000 studies that have been
  published in refereed journals and which show that GM crops are as
  safe as their counterparts."

