There are different ways to think about this:

1. Imagine what the protocol would look like without privacy (zk allows you to “sign” a computation, so just do the computation in the clear)

2. Imagine what the protocol would look like by revealing a hash of the passport only (the idea of a “nullifier”, a unique identifier that hides the data and and can be revealed to prevent replays)

The first one should already answer your question: the way you would prevent replays or portability (I use your proof) is to attach some sort of session context to your proof