As the court's opinion points out (and as others have pointed out in this thread), there are plenty of other legal remedies that can be sought against a city government that allegedly poisons its people through its water system, including voting them out of office and bringing tort claims against them.
And "you can vote them out or sue in tort" doesn't answer the constitutional question. The availability of other remedies does not make an otherwise unconstitutional government action constitutional.
Also, the Fourteenth Amendment does considerably more than prohibit abridging privileges or immunities. It expressly prohibits states from depriving any person of life, liberty, or property without due process and from denying equal protection.
That case was about a city ordinance (true, a city ordinance, not a State law that the city was enforcing, so that much is a fair point) that was inequitably enforced (non-Chinese got permits, Chinese didn't, with no other material facts being different). It was not the city providing a service itself.
> It expressly prohibits states from depriving any person of life, liberty, or property without due process
This refers to civil suits or criminal prosecutions, not the government providing services.