RFID stops working when I place the servo
Use a 3.3VDC regulator for your RFID board a small boxed DC-DC buck converter will be easiest, if linear use an LDO type. Ideally also use a level shifter on your data lines. This could be a resistor voltage divider or zener diode clamp at the most basic, FETs or a dedicated IC is a bit more involved but gets better results.