The Ethernet Mifare® RFID Reader (ER750/ER755) has been tried by us and works.
You use the little configuration app on Windows to tell it which IP and port to connect to. Our normal TCP Socket example coming with our MBS FileMaker Plugin can do the receiving and show you the data. As text encoding use Hex since you get binary data. The first 4 characters are timestamp, package type and data length followed with up to 16 bytes of card UID. And since we need only that UID, we cut it from the data block with Middle($text, 13, 32). In hex all bytes take two characters. We get the UID as hex string and can store it in a database field for later comparison.
If you have trouble getting a connection, please make sure the Firewall lets the connection coming in. Beside a FileMaker Pro waiting for connection, you could of course use a little app or script on a computer to accept it and trigger whatever connection. For example a Xojo app using our MBS Xojo FMAPI Plugin could listen with a ServerSocket in Xojo, take the request and then use data API to create a record in FileMaker or perform a query to find the record for the UID. This may even run on a little Raspberry Pi computer and if the card is accepted put power on a PIN to trigger a door opener.
Please do not hesitate to contact us with your questions.