IF any of the gear thereon is SPI, that is exactly how it should be, and there should be no need to check any libraries. Since you have had the shields working separately you already know which pins you need to use and about the only pins that can cause grief is a clash of device select pins, which should be already painfully obvious. This to the point where I suspect your problem lies somewhere else entirely. It might be simply a matter of inadequate power, particularly as Ethernet shields aren't famous for their frugality. In the unlikely event that there is a clash with the SS pins, that should be fixable. The RFID shield may well have jumper select for the SS pin.