Arts facilities are for non-profit activities. The contributions to capital costs by governments to arts facilites, whether 100% (almost never) or 10% (almost always), do not generate profits for their owners. Hence they are rarely controversial.
Large Sports facilities are almost always built for FOR-PROFIT enterprise. The contributions to capital costs by government generate profits solely for private business. Hence, controversey. Further, in any case where the private owners require governemnt money for facilities it is because they can't arrange their own financiang. If they can't get their own financing it is because banks believe the project to be unviable and a certain money loser. Hence, further controversey. Further still, in many cases, the facilities are for teams owned by people capable of paying for everything outright, but insist the government pay for some by holding everyone hostage to their plan, then stick them with any loses that arise in the future. Hence maximum controversey.
Government funding of anything for-profit is controversial, whether it's Bombardier or MLSE.
Government funding for the arts is rarely controversial, because at the end of the day, no one is turning that into profits and then saying give us more or we'll move our dance troupe to another city!
But nothing is absolute. You can't say arts funding is not controversial in Toronto in the face of Theatre Passe Muraille.