Does the song. "Silent Night" stir any feelings for you? Though I am not a believer it still does something for me.
There are many old hymns / songs that evoke emotion. Music is in the mind that hears it. Memory of people, places, events can easily be associated with music. While I'm not religious, I have fond memories of my mother when I hear 'The Old Rugged Cross'. The words have no meaning or feeling for me -- it is the music itself.
i never liked that one. then again, i'm jewish, and i feel quite inundated by all the christmas stuff for a few months out of every year, and just want to go hide. i don't feel that way about every christmas song, but that one, yeah, i really dislike it.
I read a book called Your Brain on Music and it talked about how music, a song, is a different experience for each individual. We ascribe our own meaning based on our own experiences, so we all feel it a little differently. There are a lot of religious based songs that move me, not because it makes me feel closer to some god, but for what I perceive of the song.