Interesting question that can be taken on several levels.
Can you sing a song whose 'message' you find offensive or contrary to your own views?
Or
Can you sing say a supernatural song if you don't believe in 'Ghosties and ghoulies....'
We did quite a lot of work on this in various workshops down the years.
On the first - maybe - in the right context.
I used to sing 'Blackleg Miner' a lot at one time but realised I couldn't come to terms with the idea of one group of workers fighting with another over jobs.
Nowadays I would only sing it in certain circumstances, where I could introduce it, possibly in a 'feature' or themed evening.
In the middle of the 19th century mineowners took advantage of immigrants fleeing the Irish Famine by reducing the wages of the indigenous miners under the threat of being replaced by starving Irish labour.
Prefix that information into your performance and you still have a powerful song directed at the employers rather than the 'scabs', which is what the song should have been about in the first place.
Jim Carroll