I think if you want to try it out and see, do a minimalist diet. This is what I did and then I added in foods to gauge my response
Wheat, I generally get on OK with but a bit of bloating
Rice & oats = farting all day
Most beans, including cashews and peanuts I am OK with no ill effects
Dairy is also good, apart from milk which causes epic bloatage and farting
Odd because most paleo guys say rice and oats are the most paleo friendly but I found quite the opposite. Even highly processed wheat like pastry I am OK with. I guess it's my gaelic/nordic genetics
Any large change in your diet is likely to cause bloating. Not saying it will but its pretty likely.
Your gut can adjust to the food you are eating. Stop eating wheat for a while then add it back in and you get bloated and fart all day. Most likely not because you are intolerant but because it takes a while for your gut to adjust to drastically different diets.
Think about the first time you got protein powder. Worst farts the next day because your gut isn't used to so much protein. Now for most people that goes away.