You can, in multiple ways: there's the standard single-fare train tickets that you can get from vending machines, but they carry a 1 euro surcharge over the normal fare (the paper cards still are RFID-enabled so people can open the boarding gates with them).
There's also the "anonymous" transport card that you can get for 7,50 and then pre-charge with a set amount. It will act as a pre-paid card rather than a debit card, so you can't board unless there's a sufficient amount stored on the card. But since most people then use a debit card to transfer money to their public transport card, it's not really anonymous anyway.
So most residents here choose the personal variant.
1. Ride your bike into a train
2. Wait 20 minutes
3. Roll out of the train and ride into your destination
See, it isn't that hard. What part of this process requires you to be tracked? You don't need any ID to purchase train tickets.