I have three daughters, aged 5, 7 and 9. I teach them to love and to respect, to be kind and to be good friends, but what they come across at school is people insulting, bullying and hurting their feelings. Am I teaching them a wrong approach to life?
You're teaching them how to be good people, and that always rocks (because doesn't it seem that sometimes there's a deficit of good people around?). But you also need to make sure that they know their own worth, and that being kind and nice to others is NOT a license for others to treat them poorly.
We teach our kids sympathy and empathy for others, and to stand up for those who are being mistreated. But we also teach our kids that they do NOT have to be nice to someone who is not nice to them. Instead, we have given our children permission to ignore or not be nice to those who mistreat them. They don't get to ESCALATE, but they do get to say things like "I don't care what you say about me, I don't care what you think," things like that.
When I was a kid, they told us to be the bully's friend, that the bully had a bad home life and just needed a friend. It never worked for me. What worked for me, and so far works for my kids, is standing up to the bullies. It is not my 5-yr-old's responsibility to fix another child's home life.
A few weeks ago, the bullies targeted my 5-yr-old and her best friend. The best friend punched one in the stomach when he poked her in the eye, and mine mooned them in the cafeteria when they went after her. Not the response I would've chosen, and we have since come up with some verbal retorts to use instead, but it was effective. Those kids have not said one mean thing, or done one mean thing, to either child since.
You're not wrong
What you're teaching them is great, but you must also give them the skills to understand that other people may not be as loving, kind or respectful as they are and that they'll need to be able to interact with those people.
No matter what you teach your children, some other family somewhere is going to teach their children differently and this may clash when your children meet. You can't always be there to mediate, so all you can do is empower your children to best handle any situation they may find themselves in.
On a separate note, bullying is always bad and should be reported as appropriate.
The sad reality is that most people are ill-bred, low-life scum loaded with vices and neurotic tendencies. Your job is to (A) keep your children away from their influence, and (B) teach them to have disregard for such people. The struggle to ennoble oneself is a lifelong pursuit best begun in infancy.
The proper strategy for effecting this is to inform the child of the cause of the defects in the other children. For example, in the case of a bully, usually it is because the bully is being bullied and belittled at home by their parents, or perhaps a jealous older sibling. The proper defense is to find out who at home is the source of the problem and then alienating the child from the oppressor.
For example, lets imagine the bully is Billy and we find out that Billy's dad is a drunken longshoreman who is always beating the crap out of Billy, so he is bullying other children as a result. We then have our child go to Billy and say, "Billy, your dad beats you up because he doesn't like it that you are smarter than him and one day you will have a much better job than his lousy job." If your child is successful in alienating Billy from his father using comments such as this, then all problems with bullying from him will go away.