The right way to do it would be getting
pam_nfc module working with your RFID reader. Once installed, you'll have this
pam-nfc-add command which can associate a user with a tag.
Another way is to write your own
my_getty command which supports the reader, and refer to it from
/lib/systemd/system/getty@.service instead of the original
agetty. When the correct tag is presented, your script could call
agetty --autologin username or
login -f username to complete the login process (see here for details). Your script will be very sensitive security-wise (any bug you make would likely mean a security hole).
For GUI environments, you could also look into screensavers with lock/unlock commands. You would configure autologin for a specific user, then an autorun script would immediately lock the screen and wait for the RFID reader to detect a given tag before it finally unlocks the screen. This will not be very secure if there are race conditions which give the user an opportunity to interrupt the autorun script.
Another (but also not secure) way would be to connect the RFID reader to a small microcontroller with USB interface, like Arduino micro. The microcontroller would emulate the keyboard and issue the correct login sequence (typing username and password) when the reader detects the corresponding tag. Obviously, you'd have to update the microcontroller software every time any of the users change their password, and anybody who gets their hands on the microcontroller and the tag would be able to get the password in plain text.