It quotes a legal expert at Georgetown University saying the EO is very likely unlawful and that even if the legislature passed such a law, it would be difficult and unwise to stop a company from doing a vaccine passport. "DeSantis, as a governor, does not have the power to sweep away private sector rights." Also, the EEOC, a federal agency, has said that requiring proof of vaccination as a condition of work is lawful under federal law.
According to the president of the union representing many WDW CMs (Unite Here! Local 362), "I think that he'd find that American labor law, in general, would disagree with [the order]. Employers can require drug testing and vaccination, just like a school system. *** If Disney says they believe in science and doctors and vaccines, and people getting it makes them safe, then why can't Disney require that?" The union president also said that his members just want to get back to work - safely. And if that means customers must present a vaccine passport along with their theme park admission ticket, that's all right. (This is the union talking, not Disney)
The article also talks about the difficulty with practical enforcement of the order, noting that DeSantis is not going to want to start calling the police on businesses. There's a whole lot more about the hypocrisy of taking the position that private businesses should be free to do what they want - and then trying to control them with the EO.
There's quite a bit more - this is just a brief summary. I don't see any of this as political - it involves the legality of vaccine passports and WDW's possible role as stated by a CM union president.