A question I'm occasionally asked is "how can you worship a deity that did (insert questionable or downright awful thing here) in mythology?" I think it's a fair question. When I first started looking at Greek deities and their myths, more than once I went, woah, wait, they did what? However, when I started digging deeper a few things became clear...
First, we have to remember that these myths are not holy text. They're not the word of God, or anything like that. They're not often meant to depict literal events. They're stories, and while some of them did have religious significance, many myths were told more for entertainment purposes. Likewise, we have to consider who wrote the myths. I don't just mean that they were written down by humans, but that surviving written sources were often written by educated men in particular. Often the view of a deity we gain if we only look at the myths surrounding them is not complete, we also need to attempt to look at the religious cults and folk religion that surrounded them.
We also have to consider the cultural filter with which we view these myths. Our culture is quite different from that of ancient Greece in many ways. One example that I see come up a lot is the meaning of virginity in Greek myth - Athena, Artemis, and Hestia were all considered virgin goddesses. Virginity is something that carries a lot of baggage for many in our modern culture. The whole link to purity, to how sex is sinful and dirty, and so on. Some say that virginity in ancient Greece just meant that the woman was not dependent on any man, and had nothing to do with sex. The truth is somewhere in between. One school of Greek thought was that men were projective, and women receptive, so when a woman and a man had sex, the woman was no longer wholly herself, a part of the man would always be in her. So yes, independence played a part in Greek virginity, but so did sex... just not for the same reasons sex plays in virginity today. (This is actually a huge topic in itself, all three of the Goddesses I mentioned remained virgins for different reasons... I'll have to revisit this topic in the future.)
These cultures had different morals and concepts from us today, and these are often reflected in the myths they created. Again, we have to remember that myths are created by humans, and sometimes elements of myths are perhaps more reflective of a culture's ideas truly something reflective of the deity involved. Yes, these people created these myths and included particular deities for a reason, but again, these are not divine revelations, they are human created stories.
Another thing to consider is that myths often have several versions, and of course could change through the years. Sometimes myths are in fragments, and we're trying to put a puzzle together when we don't have all the pieces. As an example, there's a myth where the hunter Actaeon sees Artemis as she's bathing, because of this she turns him into a stag and he is then killed by his own hunting dogs. I mean, that's kind of harsh, right?
Well, maybe. It depends on how much of the myth we look at. Some versions of the myth Actaeon enters into her sacred grove (or cave) where the spring is, knowing full well that this was her sacred ground, that it was off limits to him. Some say he stumbled upon her on accident, but kept staring at her when he knew that he should look away. Other myths say he had been boasting about being a better hunter than she was, and was entering into her sacred ground to hunt when he came across her in the lake. Some myths imply that he was planning to brag about how he had seen her naked. Some even speculate that in the earliest versions of this myth Actaeon was one of her hunting companions, and when he saw her he attempted to rape her.
Often myths have a deeper symbolic meaning, as well, if not several layers of deeper meaning. Let's hop over to ancient Egypt for a moment. Osiris was a god who is said to have ruled Egypt for a time, he was a kind and gentle king, he was fair, good, and the people loved him. He was eventually killed by his brother, Set. On the surface, that's pretty inexcusable.
However, let's look at these gods and what they rule, among other things Osiris is a god of the green vegetation, as well as the cultivated crops, and Set is a god of the desert. It's the same idea we see in many myths, where the gods reflect the seasons of nature, where the grain god dies, the harvest sustains the people.
Now I'm not saying myths are useless, that we should ignore them, or anything like that. Myths are an important tool to understanding a deity, and the role they played in their culture. However, you do need to try to look at these myths through the lens of the culture they came from, you need to consider how the myth was handed down, and perhaps changed over time, the role of story in the culture, what role the myth played in religious cults (if any). It's also important to understand that myths are only play a part in understanding a deity - there are many other aspects to consider besides the myths that may surround them.