My all time favorite side to eat with BBQ is a cucumber salad, it really seems to work well with smokey spicy meat. Just thinly slice a cucumber, some onion and mix it with low fat sour cream or fat free yogurt, red wine vinegar, salt/pepper. It’s super simple and really good.
Also, you could look at doing different kinds of beans, which are carbs, but complex carbs, and loaded with fiber and don’t get most people in trouble. You just have to start with dried beans, soak them overnight, drain and rinse them and pop them in a stock pot or slow cooker, cover by a couple of inches of water or stock and whatever other healthy ingredients you want. Cook until tender and you have a protein/fiber rich side with little to no cholesterol or fat