I have digestive problems with gluten, dairy, and soy, but I have no issues with eating white rice. I avoid brown rice.
For two perspectives on it, see:
I would say probably not. Better safe than sorry. Best advice I can give, is to really be strict for at least the first 30 days. After that, you can start to introducing food like rice, potato, etc.
Cooked rice is pretty benign.
Rice is not a general irritant of the gut. It is considered a non-paleo item because it is a grain, and because it has low nutrient value per caloric load. You can eat rice....but probably shouldn't.
I think this is the kind of thing that you need to do an N=1 test on. I know that a healthy gut can handle rice on occasion, but if you have an auto-immune disease or something similar then you may have issues with rice. Rice messes with my gut almost as badly as wheat even though it doesn't have any gluten. If you haven't done a Whole 30, then I'd do one and then do a rice test and see how you feel afterwards. I was never a big rice eater before I got sick though so I don't ever feel the need for it in my diet.
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