There's a good case to be made for a conscientious objection to performing at the inauguration. I'm not saying that courts shouldn't uphold the contract if the company decides to fire Rockettes for not performing. I'm saying that the company itself should agree not to do so. Many talented and reliable performers may simply have an objection to performing at Trump's inauguration. It would be a waste of talent to fire them just for refusing to perform at that one event.
Many of the Rockettes do not want to perform at the inauguration because they strongly object to the racist, xenophobic and misogynistic nature of Trump's agenda. It is unfair to expect them to take part in an act of celebration for something that quite reasonably perceive as being morally abhorrent.
Now according to sources connected with the Rockettes, dancer contracts are usually up after the conclusion of the Christmas Spectacular. There are some that are employed full time(Year Round). This basically means that the dancers who you will see perform at the inauguration are either under contract to do so or were asked and chose to take the gig. So yes, some of these women do have a choice to be there or not. But do they really have a choice?
Under all the contracts, there is always an option to decline to perform. However that would be logged as a "declined to accept" which will certainly be documented and remembered the next time jobs become available or auditions are held.
If the company in charge of managing the Rockettes signs a contract to perform at the inauguration, then the individuals must fulfill their end of the contract. Otherwise they can quit the Rockettes. Contracts have been enshrined in modern capitalism for the reason that they spell out clearly the obligations of each of the participants in the contract. There is no reason that an individual must be forced to perform, however if they choose not to perform then they have violated the terms of contract and can freely find another job. This is because they represent the group, and not the individual when performing as the Rockettes.
There are so many people that want to be Rockettes. The Rockettes organization is allowed to make their own decisions as to what events they will perform for. If someone is chosen to be a Rockette and they don't want to perform at one of the events, they should step aside and let someone participate who wants to.