Songs have always been 'hashed up' as you call it. There are numerous tunes which have a variety of different songs set to them and no end of lyrics with a number of different tunes. I hate to quote a cliche here, but it's all part of the 'folk process'.
The songs may have a valid place in history and, I agree, should be taught to children on that basis, but if they are religious songs which don't reflect your own beliefs and religion, I see nothing wrong with them being 'adapted' as well. Jenny O is right, there don't seem to be many original, new pagan songs on offer, so as I'm not a song writer either, my kids and I will just have to use what is available.