I agree that what a song means to a given singer or listener varies a lot, and I have often used non-Christian songs in church, if they fit. I sang "Somos El Barco" at a United Church Of Christ last summer, and everyone sang along; I've also used songs along the line of Blowing In The Wind or Jewish songs of peace, e.g., Havenu Shalom Aleichem or Lo Yisa Goy (which are based in scriptures shared by Christians and Jews). Not all prayers or inspirational songs used in a church service have to mention Jesus or even God in order to be compatible with that religion's beliefs.
But since it appears that Dougie MacLean did not intend this as a Christian song and many, if not most, people do not hear it as such, I probably will not use it in the Presbyterian church I often attend (because it's walking distance from my home and I like the people and their social outreach), but I might do it at the UCC church I also attend. (Heck, the songs in their hymnal and done by their choir are often as lacking in direct or specific reference to God or Jesus as the ones I used to sing at Unitarian-Universalist churches.)
BTW, since when are Scots people anti-Christian? Wasn't John Knox a Scotsman?