Seems a bit guilt-trippy to me. The "Don't want to see him sing" as opposed to "it disappoints me that you won't be there to see him sing" is what does it for me. It makes it sound like your lack of desire is about the nephew, rather than your own convictions. I don't think it's egregious of her, and I'd probably say something like, "I'd love to hear him sing in a nonreligious environment."
But, I'd probably just let this one go. She has the right to be disappointed, and you have the right to not allow that to affect your decision.
I did follow up that we would be interested in hearing him sing, but not in a church environment. This was her response, "All I want is for your family to come watch him sing. I do not expect you to stay for the service. I know Nephew will be very disappointed if you all didn't come."
First of all, I can't imagine walking out of a Christmas Eve service. I think that would be horribly rude behavior on our part. Second, every kids' Christmas Eve service I've ever been to had the choir sing throughout the service. Even if we did go, how would we determine what was the right point to leave?
I think it's time to live our values. I already take issue with MIL teaching my daughter to pray. I think it will send confusing messages to her if we now take her to a place that actively encourages it.
The first message seemed a bit guilt-trippy, but that might have just come across badly in writing and not been meant. But the bolded above screams of manipulation. This is exactly what is called the "good-cop, bad-cop" routine, like the one from the start of
Great Expectations. "If you don't do what I want, someone else with emotional/physical power over you will be disappointed, and we wouldn't want that."
I agree strongly with flikan. The sister here isn't being tolerant of the fact that you aren't comfortable in a place of worship, and is saying (initially implying, but now being blunt) that you are instead choosing not to go to slight nephew. That's pretty insulting. Would saying the same thing be accepted if you were a vegan, or devout Buddhist, and your nephew was a butcher doing a demonstration of highly-technical meat preparation at his butchery? "I just want you to watch him set up, I don't expect you to stay for the meat carving part. Sure, it's in a place you aren't at all comfortable in (a butchery), but if you really love nephew you'll do it for him."
It's important to stand your ground and be clear about your beliefs when they aren't the same as your family's, to help make it clear for them and so everyone can respect each other. I think your response about hoping for a solo performance made it clear that you do indeed want to see nephew sing. But even after this, his mother is still trying to manipulate you into going to the church, so I don't think she seriously thinks you don't want to see him sing. I suspect there's something else here--maybe she's worried the audience won't be very large and he'll be disheartened or something. But whatever it is, I think JenJay's advice is pretty good. I'd ignore any further guilt-trippy, manipulative texts from the sister here, or keep responses to, "Yeah, I wish I could hear him sing--he's so wonderful! Please give him love from me!" without addressing her impolite accusations.