Oh, piffle. This is getting widely reposted. Gluten free foods, as realized by commercial producers, end up being chocked full of sugar and crap. Going gluten-free is not going to rob you of nutrients or fiber, if you are replacing breads and cereals in your diet with good-quality GF options. Often the GF options, if baked with sensible amounts of sweeteners, are nutrient-packed beyond regular breads (my midsection can attest, when I was forced to go GF). So, you eschew the Captain Crunch for gluten free granola? That's bad? Well, for your wallet, yes (you can make it yourself for pennies on the dollar). But otherwise, it's a win.
Look for better studies than this.