Boy, bad business sense letting a personal peeve get in the way of serving the customer. The only thing I would have done, as the owner, is inform the customer that I couldn't warranty the work with those strings. But I'd put them on with a smile. He can't be loosing half as much on string sales as he is with a poor rep.

BTW, I wouldn't request the apology as an ultimatum, that will only get his back up. I would go in there and say something like "look, I understand you don't want to carry my strings, and that's fine, but I think you're out of line talking badly about me behind my back and treating me like dirt. Let's not let a little thing like strings ruin a good customer/owner relationship." When he tells you where to go (which I'm certain he will based on your description of his character) then tell him you have no choice but to take your business elsewhere, thank you.