The modern world understands religion as doctrinal – that is, ruled by its sacred stories and words. In contrast, our relationship to mythology is distinct from the way that, for instance, a Muslim would approach the Koran or a Christian their sacred texts; our stories are not revealed to us by God, but were created by man ancient poets and writers in their attempt to approach the divine. Greek religion is constituted by a dialogue between different mythologies reflecting poetic imagery and the religious practices that surround them. Mythology is related to action and relationships, but it does not tell us what to do.
The ancients wrote of the immorality of the Gods in myth. Plato wanted these myths wiped out; they were, he claimed, the lies made up by poets. Some myths are violent, and some are sexist, much like the culture they came from (and the culture we live in!). However, simply depicting them in myth does not endorse them. By raising these issues, our religion acknowledges their impact on our world, and provides us with a framework for dealing with them it recognizes all aspects of human life and how best to deal with them.
As with any mythology, the key to understanding is to read between the lines. Myth attempts to explain profound truths – truths about humanity, truths about the Gods – but by necessity, it can only do so using our flawed mortal language. The Greeks knew the Gods as integral with the world around them and, in their own language, from their own cultural view, they tried to explain that relationship. There is truth in the myths.