I believe that this falls under the heading of interpretations of the Equal Access Act, namely that "Student religious groups at Federally funded public secondary schools have the same right of access to school facilities as is enjoyed by other comparable student groups. Under the Equal Access Act, a public secondary school receiving Federal funds that creates a "limited open forum" may not refuse student religious groups access to that forum. A "limited open forum" exists "whenever such school grants an offering to or opportunity for one or more noncurriculum related student groups to meet on school premises during noninstructional time."". A musical performance sponsored by the school sounds like a noncurriculum activity held on school premises during noninstructional time. Thus, banning religious songs would fall under a general suppression of religion rather than avoiding promoting a state religion.
There would, of course, be a caveat that the school should not selectively allow such songs based on dominant religion, and the school should not be able to mandate participation. As was noted in prior answers, "voluntary participation" in schools is seldom terribly voluntary. If your coach is leading a prayer and most of the team is joining in, you are likely to feel coerced to do so as well. And, arguably, if religious music is allowed, any religious music should be allowed, so a school that introduces the "Hallelujah Chorus" to their holiday program should be as open to allowing for Jacquie Godden's Kwanzaa songs to be performed (and yes, this opens us up to all sorts of murky ideas of "equal representation" leading to no one getting much of a slice of the pie, and whether "historically significant" music such as Mozart or Bach, often paired with the dominant culture/religion, could be argued to be more "appropriate" than Adam Sandler's "The Chanukah Song").
As a former Choir geek, I'd also say that a lot may depend on how much this falls under the auspices of a "curriculum". If this is a concert put on by the choir, the teacher has the right to make their curriculum, where I believe they could be under fire if their music was overly religious in a way objected to by the populace, but I don't believe they have any legal requirement to include religious music even if requested. If this is something more like a school talent show, where students submit acts, I believe that there is a much stronger case for the students to argue discrimination if any songs related to religion are banned, the same as if a school deemed that the talent show could have no jazz or hip-hop music because it has black influences.