The routine means for enforcing discrimination in everyday life is the ID card, which everyone is obliged to carry at all times. ID cards list the official 'nationality' of a person, which can be 'Jewish', 'Arab', 'Druze' and the like, with the significant exception of 'Israeli'. Attempts to force the Interior Minister to allow Israelis wishing to be officially described as 'Israeli', or even as 'Israeli-Jew' in their ID cards have failed. Those who have attempted to do so have a letter from the Ministry of the Interior stating that 'it was decided not to recognise an Israeli nationality'. The letter does not specify who made this decision or when.
This was published over ten years ago and Shahak has been dead for about 4 years now but I am not aware of any change in the Israeli (or is it Jewish) position.