IMHO, "You Raise Me Up" does not have to be religious in meaning.
Nice thought you interpret it to say - both are nice IMO - And maybe people do separate it from the religious implication. But this is 'sposed to be about the entire student body. And there are plenty of songs that do not have that connection that fit everyone.

"You Raise Me Up" is written around that meaning, not just a mention in a song. It is the song.
This little light of mine, Swing low, yes, you could take these songs and make a different meaning then intended by the "author" but people are likely to interpret them as religious songs.
What would you say the percentage of people listening to it to find out the meaning would interpret it to be? Your are right, you don't have to,
but most do. A cross sometimes is not interpreted / used religiously, but it more often than not will leave people thinking religious. Good or evil.
IMO, Cindy Lopers song "True Colors" even used for the 8 billionth time show more respect to the ENTIRE student body. You can't please everybody all the time, but when there are a number of options that are readily available and do not have to be "re-themed" it is just courteous to those other students who
may or may not take offense, but why run that risk when it is not necessary.
When the opportunity is so prevalent to advocate for peoples rights, I think the steps should be taken. It is not as though there is a loss of good songs out there that "fit the bill."
