We have a variety of this problem, in that in the UK we have an established church (state schools have by law to have a mainly Christian assembly) and for historical reasons practically all private schools are also Christian (and are often behind with the recognising that not all their students are from Christian families, to boot). We're secular humanists and atheists. So we were pretty much always going to have to send DS to a school that would teach a religion we don't share. We dislike it, but not quite enough to homeschool just to get out of it, that being the only alternative! And DS is precocious in his consideration of such issues, and now more than capable of enjoying Bible stories, thinking about the moral and ethical aspects of what he's being told, while being quite clear that people believe different things. I was actually more concerned about his taking part in the nursery Nativity play (singing "Jesus is Lord" etc.) when he was too young to have completely sorted out fact, fiction, and people believing different things.
Of course our disadvantage of having no alternative is also an advantage: many people in the UK are in the same position and schools have to expect it. In your situation, TBH, I think I'd be asking the school. Nicely, of course, e.g. ask the head "we think your school is fantastic, and we think our DD would benefit from learning about Lutheranism, but we have to say that we aren't Lutherans ourselves. Is that a problem for you?" Point is that if you've asked "officially" and been told it's fine, it's easier to feel entitled to be there than if you just keep quiet and wonder, and if by any chance the school really doesn't want non-Lutherans as parents, you're probably better off knowing that and not sending your DD there!
