Greek religion demanded of its adherents no more than participation in traditional forms of worship. It was free from dogma, and a concept of faith was alien to it. There was, before the coming of the sophists, no "belief" in the gods in the Christian sense of the term: theous nomizein describes the performance of ritual acts, predicated on the unchallenged assumption that the gods exist and demand veneration. Since the gods are also the guarantors of the stability of the social order, and since their displeasure would disturb it, the state tried to enforce divine worship through its customs, laws, and institutions: but neither the state nor the priesthoods entrusted with the administration of cult and ritual ever displayed any interest in enforcing uniformity of religious belief. Moreover, the gods themselves were thought to be concerned only that men pay them the customary respect owed them and offer the sacrifices that were their due: human morality, so integral a part of the Jewish and Christian eligions, remained a matter of indifference to the gods of the Greeks.Ostwald goes on: 'This meant that the established religion was intolerant only of attitudes that tended to undermine the public worship of the gods.' He gives some examples: Xenophanes and Pindat were both tolerated, despite protesting the immorality of the gods, the absurdity of anthropomorphic representations of divinity and disgust at the stories of gods eating the flesh of Pelops. On the other hand, though, 'Anaxagoras was charged by Dopeithes with having committed a crime against the state' for claiming that the sun was only a fiery stone in the sky (if this idea gained currency it would 'detract from the sun's divinity and thus from its worship') and Protagoras was expelled from Athens and had his books publicly burnt in the agora for declaring that he did not know if the gods existed or didn't exist.
Similarly, here is Mario Vegetti ['The Greeks and Their Gods, in J P Vernant The Greeks (University of Chicago Press 1995), 256]:
These absences make it difficult to speak of Greek "religion," at least in the positive sense in which the term is used in the context of monotheistic tradition. The Greek language does not even possess a term whose semantic field coincides with that of the word "religion". The nearest term, eusebia, is defined by the priest Euthyphro in the Platonic dialogue named after him as "the care (therapeia) that men have of the gods" (Plato Euthyphro 12e). In this sense, the term covers the punctual observance of services in order to express respect toward the gods, during which proper signs of homage and deference are displayed. These services usually took the form of votive and sacrificial offerings. The Greek equivalent of the word "faith" is equally weak. In everyday language, the expression "to believe in the gods" (nomizein tous theous) does not indicate a rational conviction of their existence (as it will come to do in a more developed philosophical language), but "to respect" or honor the gods by performing certain acts. Nomizein thus comes to mean the same as therapeuein: to devote the appropriate ritual care to the gods.That is to say: 'we do not ask that you believe; we only ask that you act as if you believe.' This may be better than 'we demand you both act as if you believe and actually believe, too'. But then again: 'we ask neither that you nor that you act as if you do' is not the same thing as 'we demand you do not believe, and will punish you for the public performance of ritual.' That distinction is crucial.
More from Ostwald: 'Euripidean criticism of the gods of traditional religion is born of his concern for social justice. which pervades especially his early plays and in his later plays, especially in The Bacchae, turns into an attempt to come to grips with the problem of religion as such.'  he's surely right that 'the Bacchae is a statement not on the horrors of religion -- tantum religio potuit suadere malorum is frequently cited by scholars who believe that it is -- but on the dire consequences that failure by the intellect to acknowledge the reality of divine power can bring in its train'