I have not enclosed my RFID reader, but I have attached it behind a facing board on my bar, so I scan my cards/tags against a special spot on my cabinets and it registers fine behind 3/4" plywood.
I’m using a super-cheap RC522 based reader, this is the exact one I’m using: Amazon.com: HiLetgo RFID Kit - Mifare RC522 RF IC Card Sensor Module + S50 Blank Card + Key Ring for Arduino Raspberry Pi : Industrial & Scientific