The documents that come with the RFID Reader are written by resellers of the module and have many inaccuracies in them. The issue with noise from a microcontroller is not correct, so there would be no problem with running it with the ESP32.
The only issue you need to concern yourself with is the power supply. Your diagram is not clear, are you intending to run both ESP32 and RFID reader from the battery supply? If so then you won't have any issues.
If using a AC->DC power source then you need to make sure it has a Y-class capacitor to Earth to allow AC noise to return to source. A lot of power supplies have this and there is also a bunch that don't, so if the RFID doesn't work then you need to try a different power supply.