They can't identify you, provided that they don't pair that data up with anything else. Eg just a few trips where you didn't turn your phone location off on the bus would be enough to know which card is yours. Even if you turn your location off every other time it wouldn't matter. Or your phone service provider can do that even with your location set to off.

Don't the plastic cards cost extra?

How do you add money to the card? Here in Denmark we have a similar thing, but the only way to top up your card anonymously is through cash. Or do you have prepaid throwaway cards?

Here in Brazil they deprecated and outlawed NFC transportation cards that are not associated to a social ID. They can track you as much as they want. Luckily there are still cash payments and subway paper tickets but that might go away someday.

One of the most ridiculous thing about this country is that anonymity is not a right according to the constitution.