Incineration
Incineration as in "Incineration is a waste treatment process that involves the combustion of organic substances contained in waste materials." See https://en.wikipedia.org/wiki/Incineration
Seriously. They sell waste treatment for the neighboring city states. As long as the "flame burns strong", their economy is successful.
The only waste they don't process is dung. Dung is not only blasphemous, it is also smelly.
Note that in real life, certain religious beliefs have originally originated from economic reasons. At some times, it has been easier to enforce certain "trade/economy regulations" by disguising them as religious laws.
The fire can probably last until environment protection law are enforced (possibly though diplomacy/war/violence from other city-states). They might keep it up despite that by employing filters, catalytic converters - or by producing electrical or mechanical energy, which is so valuable to the global economy that the pollution is accepted.