Belo yes, there is still a lot of discrimination/prejudice in Israel.
There are divisions between the Ashkenazi (Eastern European) Jews and Sephardic Jews (darker skinned Jews from mainly Arab countries, such as Morocco, Yemen, Syria etc).
The state's original "builders" and statesmen, army generals were nearly all Ashkenazi Jews, who were usually more educated, considered more cultured etc. Broadly, coming from Western Europe where education was probably more accessible and possible. Therefore, mainstream society until pretty recently was "built" using this bias of supposed superiority.
So you might presume that your Dr, lawyer and businessman might be from Ashkenazi stock and your builder, greengrocer and bank worker (but not bank manager) would be Sephardic. So programmes, radio etc would play music or feature characters using these general stereotypes. Sephardic Jews (again using stereotypes to demonstrate the point) would listen to more Arab-sounding music, think belly dancing versus Fiddler on the Roof style violins, say. One was considered "higher" culturally than the other. This is changing however and I think the younger generation there are much more equal and non-judgemental and will even out in future (although not completely).
Unfortunately, the Ethiopian Jews who were airlifted to Israel and, in the main, extremely religiously observant, were treated very badly, which can only be racism, I'm afraid.
You can see these stereotypes played out in the kind of jokes you would hear (in the late 80s/90s anyway) : Moroccans were the stupid ones, Persian (Parsi) Jews were the stingy ones etc.
Also, huge divisions between religious and non-religious groups, most people are very secular but religious groups hold a lot of power for their small numbers in elections, because of the proportional representation system, where a party with under 10 seats can hold the balance of power when trying to form a government. Therefore, they can make deals with the bigger political party which keeps religious bias higher on the agenda than it should be.
Sorry for the long essay, just my opinion obviously, but I did live there for nearly 10 years; it's complicated just like all things in the Middle East
(hope it makes some kind of sense!)