I don't think it's possible in some situations. In a lot of cases, what you do for a living defines who you are as a person. I know it shouldn't be that way, but it is.

For example, in most cases, if a woman is a stripper, she's viewed differently than a woman who is a teacher whether she's at work or not.

It would be fair to say that most people take their values to work with them and therefor their values are applied to their tasks.

In this instance, the employee has the right to think what he/she likes, but if her personal beliefs impinge on her ability to do her job, then he/she is in the wrong profession.

Time to get a new job then, I agree.
It is unreasonable to expect your job to change for you.