No it does not. Apartheid is a specific form of discrimination, where people are categorized according to race, and differently with different rights. All Israeli citizens, regardless of race or religion, have the same rights. Black Ethiopian Jews marry white Jews, and any Israeli citizen can stay or eat where they wish. The Israeli Supreme Court prohibited limiting home sales to only Jews.

If there were apartheid, a non-Jew could never serve in the government or represent Israel

You are referring to checkpoints in occupied territories, and they apply to anyone trying to get through. Those are not Israeli citizens and they do not want to be. With all the terrorists trying to enter Israel, what nation would not do the same?