To add to this tremendously important subject : in the Netherlands, it's the same: public pools often have a "no shorts" policy. This is because teenage boys often wear baggy shorts to the pool with their boxer shorts sticking out on the upside (similar to the baggy trouser fashion). Yuck. So it is a hygiene matter.
I don't expect any problems for adults in shorts, but if you bring teenage-ish children, they MIGHT respond to that. I'd definitely risk it, you're not buying speedos especially for your Disney trip, right?