When I was a child my parents read Grimm's fairy tales to me frequently. I remember having favorites, mostly the princessy ones, and asked for them a lot (though I don't remember choosing to re-read them myself once I could read). Simultaneously they were teaching me not to lie, to steal, to cheat, etc. Like others have said, I never noticed any conflict. It never occurred to me my parents were in any way condoning or endorsing fairy-tale behavior. It never came up in conversation about how not to behave, either. The fairy tales just were, phenomena unto themselves, divorced from everyday reality.
It wasn't until I was in my twenties and started to read Puss in Boots to a friend's child that the two parts of my understanding collided. I have a nurturing temperament: in all my interactions with her kids I tried to give them information about the world and how to behave in it, and here I was reading a story where the protagonist tricks and kills a perfectly innocent giant so he can steal his castle and lands. I was appalled, so much that I couldn't even finish the story.
Skip forward to when I had my own child, and this unexamined distaste for children's fairy tales was still with me. I did not consciously choose to leave them out of her education, but night by night, when I read her stories, or picked books from the library, I somehow never chose traditional fairy tales.
And this turned out to be A Bad Thing. Because literature is full of references to other literature, and stories are told in opposition to previous ones. Even outside of literature, the fairy tale archetypes are well-known and powerful and useful for discussing human behavior. Some are culture-specific, some resonate across different cultures, but my daughter is missing almost all of them. She has lost points more than once on tests because she was never exposed to this underlying layer of archetype. (E.g., "Why is chapter 5 of The Bridge to Terabithia called 'The Giant Killers'?" She thought it had something to do with really big killers.)
If I could do it again, I would read these things to her starting when she was one or two. I would use a different tone from when I read her other books, always start with the words "Once upon a time," and just present them neutrally as information. They do have their own morality, but it's one where giants and witches are always bad, and it's okay cheat and steal from or even kill them for no reason. As Wiccans and NBA stars would agree, it's clearly not acceptable in our world to discriminate against whole classes of people... but I would save discussions about this for other material. I would make very sure I found this other material, however -- especially to counter the Cinderella story -- and make sure we had those discussions.
Similarly, with regard to the atrocious punishments found in fairy tales -- another reason I didn't want to read them to her -- I think it would have been okay to tell her about the red-hot shoes (e.g.) starting when she was too young to grasp what this meant. Perhaps this would have made her tougher later on with regard to her feelings for characters in stories, and not so upset when bad things happened to them. (See my question How can I help my ten-year-old not be traumatized by the deaths of characters in books? from some time ago.)