Catholic Musicians at Protestant Churches

Gavin posts about a job opportunity at a Protestant church. I think he raises some questions which are worth considering for all liturgical musicians.
1. Under what circumstances is it ok for a musician of any faith to take a permanent or semi-permanent position of leadership at a church which has conflicting beliefs?
2. If a musician takes a position at a church with different/conflicting beliefs, should he allow his own beliefs to affect his musical choices? If so, in what way?
3. To what extent is it legitimate for this musician to participate in their worship service? (I suppose this depends largely on his faith and the faith of the church he's working in.)

I think we can all agree that being a liturgical musician, especially one in a position to lead a congregation and make important musical choices, is not "just another job," in the way that playing for a party is. I think we can also agree that, while it is certainly a good thing for a Catholic musician to be a witness to his faith, it is not part of his job description to convert the congregation for which he works or tell them that their Eucharist is not valid (assuming that they believe in the Real Presence).

I know that some of you out there, especially Mary Jane at Sacred Miscellany, currently or have in the past been a Catholic musician at a non-Catholic church. I know I have been called upon to play at Protestant weddings, and I always wonder how much to participate in the service. It is important not to distract those around you by your lack or participation, but leading them to think that you believe as they do could also be detrimental. How do you handle it?