Disney's argument likely will have little to do with the state constitution. Disney probably will frame this as a violation of the 1st Amendment:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech [emphasis added], or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
Citizens United suggests that corporations such as Disney have rights that are protected by the 1st Amendment.
A reasonable argument can be made that the State of Florida passed a law that abridged Disney's right to free speech.