Take it up with your city council, if they're the ones require a smartphone to pay for parking.

But also, you're going to have to be more specific about what tracking you're worried about. Cell towers need to track you to give you service. But the parking app only gets the data you enable with permissions, and the data the city requires you to give the app (e.g. a payment method). So I'm not super clear what tracking you're concerned about?

If you don't use your smartphone for anything but paying for parking, I genuinely don't know what tracking you're concerned about.