True, Lester was definitely nuts, and shouldn't have got that position in any case, no matter what.
The main problem is Kirk agrees with her that the situation (whatever it was), was unfair, which suggests there was some type of sex based restriction in place.
Otherwise everything else seemed normal to Fed citizens--they considered their government the ultimate in freedom.
BTW, Star Wars had The Republic, which was called a democracy. It was sort of like the Federation, prosperous, freedom--the main words thrown around was freedom and democracy.
Ironically, that one got manipulated into turning into an Empire with a dictatorship, through the so called democratic process.