Yes. we will disagree because based on the legal discussion going on elsewhere about this situation
there may well indeed be a constitutional issue here. Specifically, precedent that limits what an employer can dictate employees to do or not do
when they are not working and are outside company property. One notable quote on this from a constitutional scholar:
"When can an employer legally discipline or terminate an employee for their online behavior? This will vary from state to state,
as more states are passing all-encompassing "off duty conduct" laws that prohibit, at least potentially, an employer's ability to discipline an employee for online actions. That does not mean employers are without any mechanism for regulating an employee's online activity.
An employer has the right to discipline employees for their online behavior
during working hours; an employee is at work to do work, not to send Twitter updates, post on Facebook or maintain a blog. The one caveat to this rule is that employers must be consistent in enforcing this social media policy; an employer cannot discipline employees when they make negative comments about the company, but ignore other non-work related activity while an employee is on the clock.
Second, an employer can, and must, intervene when an employee's online actions are placing the employer
at legal risk -- such as betraying confidential information (
ed: as others have observed, can Disney seriously make an argument that disclosure of the fact Muffy plays Donald Duck is putting the company at legal risk?
), or violating the Federal Trade Commission's rules on endorsements of the company's products, or threatening or harassing a co-worker. Third, employers can act when an employee has crossed a line and acted disloyally. Complaining about your boss or your pay isn't disloyal; telling people that the hospital where you work is unsafe would be disloyal (
ed: see above comment - is disclosure that a character is really just an actor in a suit being "disloyal?"

)- though if there are real safety concerns raised, the employer needs to address them.
Bottom line: again, this is a knotty situation by virtue of the ambiguity of how far Disney is trying to reach into the
private, off hours behavior of CMs.