I'm going to weigh in on the Agree side with the qualifying statement of it that actor wants to succeed to the utmost at their craft. Of course it is the actor's personal decision but I feel the definition of an actor clearly outlines what is in question. The person is simply acting and not in any way demonstrating that they believe in whatever concept it is they oppose.
I find it ridiculous when an actor makes an ordeal out of a role. She or her agent could have clearly said "no thank you" and left it at that. It did not have to become the spectacle it has become. Having said that, actors play a part that should have nothing to do with their real lives. That is their purpose, to entertain while pretending to be someone or something else.
If a job came up in an organisation whose work or values were controversial to your own, you shouldn't be forced into a contract with that company. That must be some form of slavery. If an electrician was offered a job in a death row prison but disagreed with capital punishment, they shouldn't be forced into taking the contract just because they're an electrician.
Actors have added pressure because their work can influence audiences and they should have the freedom to choose what messages they are representing. In this example, the actress does not wish to support the ideologies of psychiatry because it is controversial to her religious beliefs, there should be nothing wrong with her turning down that job. Perhaps the problem is more with the role of the media than the role of actors.
I think I remember the episode of Fraiser we are talking about, it's the one where all the Cheers cast showed up. If I remember this correctly it was kind of silly for Alley not to do the episode. Why it wasn't about Psychiatry in the least, it was about everyone gathering for a going away party for Cliff. Now I know that maybe Alley felt that way, but she was on Cheers for years with Kelsey Grammar with no issue so what was the problem now? Yes I do think however it should depend on the script though, so I an't fault her too muh.
It's ludicrous to think that an actor should be forced to play a part against their religious beliefs. If that role went against what she believed in, there is no reason she should have been forced to take it. This is the same for many other issues in life. People have the right to choose what clothes to wear, what brands to purchase, which stores to shop at, and of course, which church to go to, among other things.