I looked over the charter. The main section on the district's powers is section 9 on pp.26-30. The listed powers are (1) to engage in legal proceedings (2) maintain a corporate seal (3) own and dispose of property (4) lease facilities (5) exercise powers of eminent domain (6) powers relating to reclamation, drainage and irrigation (7) water and flood control (8) water and sewer systems (9) waste collection and disposal (10) mosquito and pest control (11) airport facilities (12) recreation facilities - this one allows the district to own, acquire, build, maintain and operate parks, golf courses, museums, convention halls and all other types of facilities (13) parking facilities (14) fire protection (15) advertising (16) transportation (17) public utilities (18) conservation and sanctuaries (19) issue bonds and (20) other powers and research and development - this is a catch-all that allows the district to develop and utilize new concepts, designs and ideas.
I'm not finding any basis in the powers listed above for prohibiting a business operating in the district from adopting health mitigation measures.
Section 23 "Planning; Building Codes; Safety Regulations; Platting and Subdivisions; Zoning" has subsection (9) that states : "Any regulations adopted pursuant to the provisions of this section relating to safety, health, sanitation or building safety shall prescribe standards at least equivalent to the minimum standards in applicable statewide regulations protecting the general safety and welfare of the public." So I guess if the state somehow declares flu-type disease mitigation measures detrimental to the general safety and welfare of the public, this might fit. I'd like to say that last sentence was a joke, but . . .
I think you would be well within your rights to ask what in the charter gives them authority for what they said they were going to do. If they give you one, get bold and ask for the section that lets them control Disney's content.