It is not ILLEGAL to carry a concealed firearm at WDW, assuming you have a valid Florida, Florida non-resident, or other state concealed carry permit that has recipriocity with Florida.
HOWEVER, if your concealed firearm is detected, Disney will ask that you leave, and if you do not in a prompt and orderly manner, they can (and probably will) arrest you for tresspass.
That being said, given the overall security level at the park, the high likelihood of (me at least

becoming at least mildly intoxicated, and the difficulty of secure storage of a firearm doing all the things you do at the parks, I CHOOSE not to carry. If I was just going to walk around, stay stone cold sober, and had others to protect, then I might reconsider.
I have had their security folks ask that I check my folding knife. Very quick, easy, and relatively painless. Just glad I remembered to pick it back up at the end of the day!
I agree that the bag checks are more about getting other "contraband" like glass bottles, drug paraphenalia, a stashed wedding gown, or counterfeit merchandise. Not a big deal since it is usually an issue only once, maybe twice a day. Heck, if it is raining or chilly, my low profile backpack (especially since the jacket is most of the bulk) can be worn under a jacket and no one is the wiser.