[1] A citizen was considered to be any person born of Greece, white and male.
https://en.wikipedia.org/wiki/Athenian_democracy
I doubt that the Athenians had the present-day concept of "white people". Wikipedia says that citizens "had to be descended from citizens", so maybe at least in a certain era nobody known to be descended from people coming from outside of Athens could be a citizen.
https://en.wikipedia.org/wiki/Athenian_democracy#Citizenship...
Edit: looking at one of the references, it seems that there was a year when explicit citizenship lists were drawn up based on all free men who lived in Athens (maybe with some kind of ethnic exclusion at that time too?). From then on until Pericles, children could be added to the list if their fathers were on the list. After Pericles, children could be added to the list if their mothers and fathers were on the list.
Most importantly, while there were a few questions settled by referendum where all citizens could vote, most were settled by randomly allotted juries. This meant there was little advantage to forming political parties around popular demagogues, or run well-funded propaganda campaigns.
Athenian democracy got knocked down many times and came back every time, except the last. The second-to-last time, a bunch of immigrants had fought for the liberation and restoration of democracy, and some leaders argued forcefully that they should be awarded citizenship for this. But they didn't get it, the existing citizens voted against.
The reason democracy finally failed was probably this. The Athenians knew (especially the poor) just how unusual and lucky they were to have political freedom, so they were fiercely protective of it - and didn't want to dilute it by sharing it. Eventually a large part of their society had so little stake in democracy that they didn't bother to restore it.