The important thing to remember is that 'Brit' is a very informal word. It's used in informal contexts because the adjective+noun combination "British people" is cumbersome and the 'official' term "Briton" can sound formal and awkward. Serious newspapers use the term 'Briton', while the gutter press and tabloids say 'Brit', for example. The nearest equivalent I can think of is the way people outside the US use 'Yank' to mean American (any American). It's not exactly pejorative, but it isn't respectful either. So, like most colloquial usages, it is rarely neutral. "Russian" or "American" are neutral words - "Brit" is not. This means that the context is crucial. If you refer to someone as a Brit ( or a Yank) in an angry, impatient or derogatory tone - yes, it's insulting. But if you use it in a positive tone, "I just love the way you Brits say...", it can seem friendly or affectionate. As the other members have said : Context is everything.

I think it depends on the context. There are certainly situations in which it can be used in a derogatory manner. I, as an American, would never say the word "brit," because it does indeed sound rude to me.

In Northern Ireland it would generally be intended and understood as a pejorative term.

I would not be offended by being referred to as a "Brit" unless the context made it so.

As far as I hear it, it is neutral and I mix with the great-unwashed. 'Briton' is more broadsheet and 'Brit' is more tabloid, as Suki says. I disagree with her 'serious' (broadsheet) description and would refer to them more as 'seriously ignorant', and the real 'gutter' press. The tabloids at least have the merit of not continually preaching, and of using highly abstract words fooling their readers into thinking they understand an issue, when all they really understand is a circle of words. This cannot happen if you use concrete language like the tabloids. Orwell knew their tricks.