Arduino Nano + RC522 + w5500 Ethernet Module
If both modules use SPI then they should each have a separate pin connected to the slave select.

This lets you select which module you are talking to every time you start a communication. If the modules are well behaved then its MISO pin will be in high impedance when it is not selected instead of pulling it low or high trying to send data.

If it is not well behaved then you will need to add a buffer.