I am a youth worker and have worked with many victims and instigators of bullying behaviours. Despite this, it's still hard to come up with solutions that are practical. But I'll try....
Ideally parents objectives (of EQUAL importance) should be 1, protect you child from bullying behaviours and 2, don't let you child= grow up and exhibit bullying behaviours.
I recently attended a folk music festival that caters for families from all walks of life and it was amazing to see such a liberal approach to how different cultures, sexualities, genders and preferences are actually celebrated rather than ridiculed. I observed a trans person conducting a Trans Story time session (performed daily) where children gathered around to listen to a story read to them by a drag queen (hope that term doesn't offend anyone). No one in that setting batted an eye lid around how the individual chose to dress, parents or children. Allowing children to enter spaces that are safe and non judgemental is the best thing we could ever do for children in addressing bullying. They will hopefully pick up on the fact that differences are not important and that people who make negative judgements of others usually have their own issues.
On the flip side, I don't think it's too hard to see why some children exhibit bullying behaviours, look at the media messages on the front of our newspapers and magazines. Primitive judgements are poison to kids, they do pick up on it and they do copy it!
When I was at child the word 'gay' was used as a pretty powerful put down to people and things, it wasn't used to describe sexuality, it was used to describe negativity, 'your shoes are gay' for instance. Today I work with kids who couldn't care less if someone is homosexual or not. So I do think things are changing. In the past couple of years we have seen the gender fluid movement come into fruition and I think it's wonderful that people are rejecting the concept of making one choice or conforming to one gender type. This carries incredible power and exposure to people who are different or refuse to be judged and are comfortable in their own skin, despite what some people might say is a wonderful example of how to not let bullying get to you and to not judge others.
The end!