Surely the title sounds obvious? The other day I heard/read the question "Don't you want your children to learn to be polite?" in some context and came to think that what sounds obvious may not always be so. How we do it can be quite hard.
I do not believe that many parents today have politeness as an end in itself for the children, but my thoughts here are still based on the fact that sometimes it still seems to be more important to be polite than to say stop.
To begin with: what do we mean when we talk about being polite?
Because I don't want my children to be anything "for the sake of it" or to show others that I, as a parent, have managed to teach them a number of skills. Most people can learn that talent (but at what cost). The people I know who had the most pressure on themselves to sit up straight, eat nicely, hold hands, etc., etc., as children, certainly managed the task gallantly when they had "eyes on them", but were also the ones who were absolutely the most out of control and messy in others room.. Have you really taught the children anything about how to behave with other people then (because that was the purpose, I guess)?
Leading by example is the only way, I think. I say thank you when I'm served food at a dinner party, I ask if I can help someone who looks like they need it, I open the door for someone who can't..and all that. And I do it because I WANT to, not to show off. I don't throw food at people in restaurants, I respect different ways, cultures and contexts, but sometimes I talk with food in my mouth or sit half upside down on a chair.
I think that I thus teach (or show!) the children to be human (with all that that means) and hopefully a feeling for that thank you, an eye for when help is needed and the ability to put yourself in other people's situation and therefore see it as self-evident to open that door.
Based on that, I am sure that they can move out in the world, in different contexts and feel right and wrong. Thank and help from the heart but also say stop/now I get up and go or tell someone to go to hell from the heart. Too hard politeness can probably dampen that heart quite a bit.