Sure. But this also describes a lot of well-accepted democracies' histories.
Perhaps you're thinking of a liberal democracy?
> would argue that it was not
Sure, according to a personal definition that countries cease to be democracies any time they go to war (or more narrowly, commit war crimes), Israel is not a democracy...
> there were many other classes not allowed to vote at the time
Most democracies also prohibit children and non-citizens from voting. The term you may be looking for is full democracy. And I think most people and experts agree Israel is not a full democracy [1].
[1] https://en.wikipedia.org/wiki/The_Economist_Democracy_Index