I think post-zionists might be those that want a binational state.
Not a jewish state.
So they would change the national anthem "soul of a jew yearns" for example. Not sure what they'd want for israel independence day, maybe ceasing its practice, and celebrate the day that they G-d forbid, make israel the "binational" state. And they'd probably eventually rename it so it's no longer called Israel. If they live that long.
Since they remove the jewish aspect, they would probably lose the "law of return"(for jews). So as to be like any other country.