Disney is private property and can do what they want. A friend of mine was there with his family and was in Disney Springs. He was off-duty (works for a neighboring County SO in FL) and was carrying CONCEALED in Disney Springs (which anyone can walk in to). A Disney Security employee walked up to him and asked him if he was a law enforcement officer. He said “yes, why?” He then asked if he was carrying a firearm to which he replied yes as well. The Security Guard politely explained that Disney Springs (although open) is private property and firearms are not permitted. He offered to escort him to their security office to lock it up or he could secure it in his vehicle in the parking lot. He also asked if someone had complained or if he was printing in some way and the security guard said no, you just looked like LE. After a uniform deputy verified his credentials, he (the Deputy) walked him to the parking lot to “secure it in his vehicle” ...as far as Disney knew.
Me personally, Disney is a target for terrorism, mass shootings, etc....large groups of people in a concentrated area. If anyone can walk in, you think I’m going to lock up MY gun...hell no. And if they ever asked me, I’d take my business elsewhere. Now in the parks where they screen EVERYONE and they have Deputies at the entry and exit points, fine I’ll lock it up knowing everyone has gone through screening and they have a front line of defense. But Disney Springs....yeah make the cop lock up but any a-hole can walk in packing.
My point is...conceal it better, take your business elsewhere or just smile and agree to do what they tell you.