I would shoot a gun with Damascus barrels but only conditionally. I would want to have barrels that were made by a quality maker, originally Nitro proofed and inspected and measured by a gunsmith who understood double guns and Damascus to ensure the barrels were still in proof and not corroded or bored out. Then I would shoot them with lower pressure loads only.
Such barrels unfortunately are not easy to find and a great many Damascus barreled guns were cheap crap, poorly maintained, never properly proofed in the first place and often bored or honed out beyond acceptable limits. Therefore I don't blame anyone who chooses not to shoot Damascus ever but believe there are circumstances when it does not present a risk.