I can think of more than one way to answer this question, depending on the exact situation.
On a technical, halakhic level, I am not sure that people thinking you are a Christian when you are not, actually violates the law of îøàéú òéï (mar’it ayin). According to this law, it is forbidden to do an action that you know for a secret reason is not forbidden, but looks forbidden to others.
The classic example is if you meet you friends for lunch at a treif Burger King, and you bring your own burger from home and eat it there. Now you know that you are eating kosher, but anyone looking at you would reasonably assume that you are eating treif. This is mar’it ayin and forbidden.
Someone thinking you are Christian because you are performing in a church is not necessarily mar’it ayin, unless you are singing prayers that, in theory, reflect the Christian beliefs of the person praying. Moreoever, mar’it ayin is not about someone thinking you are a Christian doing Christian things, that is just a misunderstanding. It is about someone thinking you are Jewish (or recognizing you) and doing forbidden things (like eating treif or worshiping Jesus).
This brings us to another issue.
I am not sure I follow what it means that you are singing in a choir in church. If this means you are singing uplifting songs (not prayers) to entertain the listeners, then this does not sound like a problem. However, if you are leading prayers to Jesus, then I think the mar’it ayin issue is the least of your concerns, halakhically speaking. It is forbidden in Jewish law to pray to other gods, and Jesus is, in most forms of Christianity, a divinity of some sort. If you are in a church, leading prayers to Jesus, you are praying to Jesus, even if you don’t mean it in your heart. This is a problem. In fact, technically, I don't think it is mar’it ayin, since the person seeing you is correctly (not mistakenly) assessing what you are doing.
Assuming either that you will be doing this anyway, forbidden or not, because it is your job/you have made your peace with it, etc., or, alternatively, it isn't a prayer servince but you are just entertaining the listeners not leading prayers, then I think what you might be expressing in your question is that it bothers you emotionally to have people think you are a Christian when you are actually a Jew. Perhaps it also bothers you emotionally for people to think you are singing prayers you really mean when in your heart you are just a performer singing a song, not a supplicant leading a prayer.
I certainly understand that and would feel similarly in such a case. My advice then would be that if you feel you want to share that you are Jewish, and that this service is not actually “your service,” that might be a nice thing. I just caution that you should probably only bring this up if you feel you can do so without appearing rude or dismissive of their beliefs and their service, since this is, in fact, a church not a synagogue, and you are a guest in their institution and not vice versa.
I hope this answer is helpful,
Zev Farber, Zikhron Yaakov
Answered by: Rabbi Zev Farber