The movie is based off a comic book writer and the film is fiction not based on reality. Reality is the Persians crushed the Spartans and went on to burn Athens.
The Spartans were mostly homosexuals
They were authoritarian that is why they fought with and did not respect the Athenians
They did not believe in democracy or the Western way of life as claimed
They are not exactly the models of modern society or the advents of modern democracy
They also practiced eugenics in an effort to breed a race of super warriors. In short, they were proto-Nazis.
Still, there is something about a last stand against overwhelming odds that still fires the imagination.
Actually, the events depicted in the movie are more or less accurate, from what we can gather from the ancient historical sources. The Persians only crushed the Spartans because of Ephialtes' betrayal, and the the burning of Athens is not within the timeframe of the movie, coming later after the Persians had pressed further into Greece.
The Spartans were mostly homosexuals
Correction - the Spartans (as with most other Greeks), were homoerotic. They did not practice a "homosexual lifestyle" in the sense that us moderns think of it. Pederasty was common in ancient Greece. NAMBLA would, in many ways, have been quite at home in Athens. The Thebans had an elite band of warriors made up entirely of pairs of male lovers. It was a vice that afflicted Greek society generally.
They were authoritarian that is why they fought with and did not respect the Athenians
MOST Greek city-states at the time were authoritarian, either monarchies or under the various tyrants. Even Athens lived under Peisestratus for a while. The Athenians themselves, even under the democracy, still managed to execute Socrates, oppress their "allies" in the Delian league, even razing city-states that wouldn't cooperate with them, and kept a full quarter of their population as slaves.
They did not believe in democracy or the Western way of life as claimed
Well, "democracy" is not the end all and be all of the Western way of life. Indeed, most of Western history has NOT been characterised by a great love of democracy. Even Athenian democracy was not what we think of by the term today.
They are not exactly the models of modern society or the advents of modern democracy
And nobody has said they were. The Spartans had a LOT of serious problems with their societal ethos, not the least of which was that they were themselves an imperial state which had conquered Messenia during the Archaic period and kept the Messenians as helots - serfs tied to land and kept as third-class citizens. Young Spartan men, before their full entry into the Spartan military aristocratic society, would serve a couple of years as "secret policemen", spying on the helots for any signs of dissent, and would more or less summarily execute any thought to be subversive. So yes, Sparta definitely had its problems, and even in Classical Greece, it was viewed as a backward and regressive state.
But the point of the movie, and why we should yet be glad for the sacrifice of the Spartans (and Thebans, and Thespiaens) at Thermopylae is that they really did, historically speaking, give the rest of Greece time to get it together to defend the cradle of our civilisation from the Persians. If they hadn't done so, our whole Western civilisation might well have been strangled in the crib. Leonidas gave Themistocles time to win at Salamis, and this battle, along with Plataea, Marathon, and Salamis, were instrumental in altering the entire course of world history.