One of the biggest things that I find baffling is that a lot of (obviously not all) charity or volunteer opportunities have a religion based mission statement.
If that's what you want to do, that's amazing. I don't find a problem with teaching your kids the moral and theological code of a deity. It's provides structure and for the most part has a good message. What I don't agree with is making it seem like that is the only reason why you do things.
I don't want my son to think he has to do so many good deeds in order not to spend eternity in a fiery pit. I don't want him to think that if he makes a mistake, that his first reaction should be to grovel.
Raising a a child who cares about his fellow man should be just that. Care about other so that the receiver will be influences to spread kindness to another and the chain continues.
If one makes a mistake, separate the act from the person. Explain that your son or daughter is not a bad person, that he/she has a good heart and is a good boy/girl. However doing said act does this and makes whoever feel whatever way.
That way the child knows that they did was wrong, but doesn't identify the self as being bad. If they are able to see this within themselves, they will be able to have that grace with other people.
This can also open up a dialog as to better express their feelings, rather than acting primitively. But it also gives them a sense of taking personal responsibility.
How does this all tie back into religion?
I feel like a lot of both positive and negative actions hide behind a deity or prophet. Do good to your fellow because (blank) teaches us to. We had to punish these types of people because (doctrine) told us to.
You're creating a shadow that allows kids to hide with their actions or words.
Remove that shadow and they're left with themselves. They have to be able to identify what they're feeling, how to deal with it, and how to make it right.
Once again, I am all for following whatever religious sect you want. But you can still teach kids to take responsibility for their actions and separate the act from the self; knowing they'll be able to do the same with others.
From there your children will find grace and tolerance for other people.