CMD8 wrong response problem

I have a 32 GB Kingston SDHC microSD card which has to communicate to MSP430F2618( via SPI.I am trying to interface an microSD card to a microcontroller board (FRDM-KE06Z) using FatFS code. I only modified SPI parts for my application. Besides digging into FatFS code.

When I send CMD0 to the card the reply is correct: response to CMD0

But when I send CMD8 to identify the card the response is totally wrong (after 0xFF there should be anything with MSB set to zero): response to CMD8

I have checked:

  1. Different SPI modes 0/1/2/3, clock speeds 75kHz and 150kHz
  2. Two different SD cards (brand new 32GB SanDisk Ultra HC 1 and an old SanDisk 2GB)
  3. I do send dummy clock cycles after power, I also wait a couple of seconds before doing anything with the card
  4. Wiring is short, so signal integrity should not be the problem
  5. The same happens with and without logic analyzer attached
  6. Plugging the card after MCU pins are initialized, waiting a couple of seconds and starting the code
  7. CS timing is very relaxed (couple of miliseconds before data is sent, many miliseconds between CMD0 and CMD8)

What can be the reason my cards are failing to properly respond to CMD8, while responding correctly to CMD0?