Is it OK to refuse work duties based on personal conscience?

A couple of recent scenarios are bringing attention to just how a person is supposed to reconcile the difficult dilemma of being asked to perform or include a particular aspect of one's "job" that might be a blatant "offense" to them as individuals with specific beliefs.

A Christian county clerk in Kentucky and a Muslim flight attendant with ExpressJet™ are being 'charged' for (allegedly) not carrying out parts of their (alleged) "job duties" because of their (alleged) personal religious beliefs.  Note that I'm using the "alleged" term to indicate that these things are still being ironed out and the outcomes are unpredictable, at best.

So...what to do? In such cases when one's "job description" calls for certain behaviors or practices which can impact one's personal conscience, should they simply avoid such job opportunities?

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