In my opinion it doesn't really matter which version is used, but please don't change posts from one to the other unless there is good reason. Changing these when it isn't really necessary is more likely (than other edits) to spark an argument or edit war, and could well be construed as rude.
My take is that we should let the poster use whatever form of English they use personally - assuming of course the post is grammatically correct, readable, properly spaced, etc.
However, if you're in a post doing an edit and come across a case where you're really not sure, then please feel free to change a spelling to one you know is valid - at least that way we have an end result that is valid in at least one form of the language.
Conversely, tags should generally be US English, for consistency. But creating synonym connections between various spellings where appropriate means this becomes almost transparent to users when entering a tag.
Note: I'm a Brit, and like everyone will have some bias, but trying to step away from that - the main thrust here is that it's not necessary so why should we risk aggravating or alienating people?
A side note:
British English isn't only relevant to the population of Britain or the UK and it's other territories. The comments have provided Canada and India as examples where the local use of English is more aligned to British English than American, and having now thought about it I would assume this is also the case for some other Commonwealth countries as well, and possibly elsewhere.
And please be aware that the difference between the language forms isn't just spelling, you've already linked to the spelling difference article on Wikipedia, but check out the wider differences as well to see what I mean.
Here is an old Meta.SO post that has more depth on the subject.