Is SPI a good way to connect two rfid modules on separate arduino boards?
Its very easy. 


Set one PIN of ARDUINO as ouput pin. You will write that PIN HIGH when your conditions are matched in ARDUINO1 then SET LOW after 1 mS.
Connect that PIN of ARDUINO1 to external Interrupt PIN of ARDUINO2.
Write a CODE for ARDUINO2 such that when EXTERNAL INTERRUPT OCCURS it will set variable high indicating that Conditions is Matched in ARDUINO1.
While providing access to on ARDUNO2 check that variable status if it is HIGH grant access and SET it LOW.


This is the basic Structure you can follow using interrrupt.