I imagine a Friendly AI, I imagine a hands-off benefactor who permits people to do anything they wish to which won't result in harm to others.

Yeah, I like personal freedom, too, but you have to realize that this is massively, massively underspecified. What exactly constitutes "harm", and what specific mechanisms are in place to prevent it? Presumably a punch in the face is "harm"; what about an unexpected pat on the back? What about all other possible forms of physical contact that you don't know how to consider in advance? If loud verbal abuse is harm, what about polite criticism? What about all other possible ways of affecting someone via sound waves that you don't know how to consider in advance? &c., ad infinitum.

Does anybody envisage a Friendly AI which doesn't correspond more or less directly with their own political beliefs?

I'm starting to think this entire idea of "having political beliefs" is crazy. There are all sorts of possible forms of human social organization, which result in various outcomes for the humans involved; how am I supposed to know which one is best for people? From what I know about economics, I can point out some reasons to believe that market-like systems have some useful properties, but that doesn't mean I should run around shouting "Yay Libertarianism Forever!" because then what happens when someone implements some form of libertarianism, and it turns out to be terrible?