If you want information about what foods do and do not contain gluten, go to Celiac sites. There are good ones out there, which have much more complete information than you are getting here.
Plenty of real foods, even low carb real foods, contain gluten. Look on a package of sausage and see whether it contains any of the ingredients mentioned. Many, if not most, sausages contain gluten. You would have to find a brand that does not. Applegate Farms and Boar's Head are good at labeling for this.
Going to buy some fish? Even in the fish counter, much of it has been frozen and then thawed to put in the counter to sell. And guess what most places do when they commercially freeze fish or shellfish. Dust it with a non-visible layer of flour to keep it from sticking together as much. This is especially true of shrimp. So either buy fresh and never frozen, or you have to beware. Trader Joe's seafood products are specifically not treated that way. But a regular grocery store? Forget it. And imitation crab, which is roundly believed to be fish actually contains significant wheat.
Blue cheese made in the U.S. does not contain rye. Made elsewhere, it may. Wine produced in the U.S. should be fine, but cheap wine produced elsewhere may not be, as it is often filtered with grains -- particularly wheat.
Also, Celiacs know that if you are buying food, Kraft and Conagra will always list ingredients such that if you know what you are looking for, you will be able to tell from the label whether the item contains wheat, rye, barley or oats, because they will tell you if the preservative in the can of tomatoes is sourced from something that is a common allergen or cannot be eaten by Celiacs.
Before being diagnosed with Celiac, I ate low carb years ago. I got a lot of gluten when I did too. Not in Frankenfoods or processed foods. I loved making stir fries. My husband and his brother would eat it over rice. I would eat it plain. That was soy sauce. I ate fish bought at the regular grocery store that had been processed. I ate barbeque, without worrying about the contents of the sauce, as long as it was low carb.
Conversely, rice, corn, potatoes, amaranth, quinoa, buckwheat, cane sugar, honey, arrowroot, tapioca, millet, certified gluten free oats, sorghum flour or syrup, and teff are all whole, gluten free foods and not garbage, but they are all high in carbs. Most are higher in carbs than wheat, rye, barley or regular oats. In fact, what makes those things so great to bake with is the fact that the protein content is high -- the gluten, which gives the grains certain attributes that other grains do not have, making breads have air pockets and making them stonger and tough and stick together instead of crumbly. Because of the high percentage of protein, they have a lower carb content than these other, gluten free grains.
So no. Gluten free does not mean low carb, even a whole, non-frankenfoods based gluten free diet, does not mean low carb. And low carb does not mean gluten free. If you have to eat gluten free anyway, low carb may be easier for you than low fat, because you already live in a world of substitutions for most carby things like bread and pizza, if you want those things. But you still have to give up the others.
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