I had some time to dig into this issue and found the cause of the problem. Nothing to do with Ethernet shield but with Seeedstudio NFC library (PN532.h).
This library is using a SW implementation of SPI protocol, not the HW implementation of the official Arduino SPI.h library used by Ethernet shield.
Unfortunately the SW implementation is not compatible with the HW implementation and when you use them together and try to share the SPI pins (MISO/MOSI/SCK) it does not work.
I created an updated PN532 library that uses HW SPI and uploadaded it to GitHub - jmgjmg/PN532: Arduino Library for Seeedstudio NFC Shield based on NXP PN532 chip. Now you can use Ethernet and NFC shields sharing the three SPI PINs. See detailed instructions in readme file.
Unfortunately, this library does not work when you stack three SPI shields together. There is too much noise in the SPI lines and the data transmission becomes unreliable.