First off let me state I am not diabetic. My diagnosis is hypoglycemic/pre-diabetic. My thoughts are, any menu at Disney (or anywhere else for that matter) can be friendly to those with blood sugar issues. It is about choices, how your body reacts, and being prepared for a bad reaction (low or high).
I need to limit my total carb intake, along with sugars. I have never run into a situation at WDW or DL where I couldn't eat at a CS or TS location.
At CS locations, if I dont have a salad with a protein, I'll have a burger or other sandwich and toss the top of the bun. I used to avoid pizza, but with the multigrain crust at WDW I can on occasion (and when feeling good) have pizza since the net carbs aren't as high as white crust. If like me, you have carb impact issues, be careful with the sugar free and no sugar added desserts - many are high in carbs, some higher then my allowed daily intake of carbs. At many CS locations, items served with fries can have apple slices or carrrots as a substitute.
Snacks are my problem area at the parks. So I carry jerky or a glucerna bar/shake with me.