I think parents must definitely teach their kids about some moral issues, but you don't need religion to do that, you have way better ways of doing it.
As someone who was raised based on both religious values and values my parents though I need to know about, I can tell you religious values only work because of the fear it puts in one's heart.
I would easily hate to end up in hell, and I was always afraid that God may not love me so I always tried to be on my best behavior, so I was not being nice for the sake of being a good human being, I was nice so I wouldn't be punished by God.
Kids's brains may not be ready for serious conversations on morals, but they experience feelings and emotions with more force than adults. When they are happy, they are the kings of the world, and when they're sad, they feel like the unluckiest thing on earth.
I don't have kids, but if I someday do, I'm gonna talk to them about right and wrong, I'd tell them to be themselves all the time, but also to be aware of what impacts their action will have on others, and try to not hurt other people.
You could easily ask kids to not hurt other people by telling them that it makes people sad when you do that. Kids don't want anyone to be sad. Just work on their feelings, emotions and instincts. That's what kids need, not teachings about an unseen deity who nobody knows and every person has his/her own idea of.
Kids usually become a lot like their parents, even if they end up in a very different place in life, their instinctual reaction to everything they face will be what they have seen their parents do, not the things their parents have told them. That's why I think telling your kids anything wouldn't be that useful, let alone religion. Kids watch and learn, they don't listen and learn.