For the most part, I'd argue it's rude. I live in the state of California though in a "quaint" small town suburb an hour drive away from L.A. I have been to other states but not long enough or through enough of their entire area to tell you otherwise. This is not one of those things that flies across the board because of that identity and cultural difference that is arguably stronger than other places because of our attitude, size, access to things, etc.
My Mom hates the question: I just asked her if she considers it rude as a general, national and social rule and she said yes (I'm a college student taking a semester off and taking transferable classes at a local community college instead of my normal university for those wondering how I asked my Mom). That's her though.
I know people either so comfortable around people or so rude around them they would ask out of curiosity. We can talk about it among other people if not referring to ourselves. Now that I think about it, the rude/acceptable ratio is probably like 60/40. I know I've talked about it now and then, but it's always been with people my age and it's either about a part-time job for school (which is a little different and more obvious without saying anything) or our parents and what we think they make or know they make that we somehow found out through some means. Once you get a career, I feel like it's one of those questions you just don't ask offhand that often. The older you are the more likely you hate the question I think too.
Like others said, there are certain contexts it's acceptable in and around certain people and that might differ from here to Britain, in which it sounds like there MAY be no acceptable contexts.