Rfid reader and SD card shield won't work together
SD cards (or really their breakout boards) don't tend to obey the rules with regards to SPI. In particular the MISO pin isn't set to high impedance when the slave select is not selected.

You can fix this with a tri-state buffer that you feed the SD card's miso line to and controlled by the slave select. The output from the buffer goes to the arduino's MISO.