Scots by birth and country I've lived in for over 30 years, but spent the other half of my life in England, Jim.
I do need a haircut, but then so does most of the population since lockdown! (If they still have hair to cut!)

I'm a big fan of Burns' poetry and song, and have heard seen and heard at least some of the Merry Muses performed. No, I wouldn't find that poem offensive, nor the other alternative version of "John Anderson, My Jo" but they would be unlikely to be sung in the middle of an average folk club night: more likely reserved for the Burns season (which here goes on for about 6 weeks from soon after Hogmanay until near end of February!)
My husband belongs to a couple of all-male Burns clubs, where such songs maybe get more of a regular airing than they do in mixed company, although I have several female friends who sing that other John Anderson with great relish! Not one I do myself, but not for any prudish reasons - just that I know others do it better.