These days, you'll have to keep the plastic in some kind of metallic sleeve. The RFID chip in US Green Cards, and I imagine passport cards as well, is designed to be readable from across a room.
An iPhone can read the RFID but you have to know that it is NOT where the icon is, but actually on the backside of the hard thick page (or something, I forget).
As someone who has a passport card, I can confirm it definitely has an RFID chip in it. Ironically they come in a protective sleeve.