I don't remember many people taking offence to Little Britain at the time and I do think things have changed massively over the last couple of decades. I felt similar to BristolEcho, I thought Little Britain was funny for a couple of episodes till it became clear that the same jokes got recycled every week.
Little Britain was massive in the gay community because it was the first show where a gay man satirised gay men and we were laughing with rather than at him. I believe that at the time the general idea was that we were laughing with the characters in recognition rather than at them. The show was massively camp and by the LGBT community at least the characters where considered with affection. The stereotyping was offset by absurdist comedy not far from Monty Python which created a distancing effect and which made it clear that this was its own universe, not dissimilar to The League of Gentlemen which came a later later (and which also is being pounced on.) The stereotpes got pushed so far that they the characters became somewhat surreal. It really hasn't dated well and I didn't think it was all that funny the first time round but I also can't pretend we all were massively offended by Little Britain back then.
Rather than singling out Little Britain, I have a bone to pick with a comedy genre known as "character comedy" which is particularly popular in the UK. I always there there is a degree of cruelty to sneering at someone for whatever reason which is at the root of that type of comedy, combine with a self congratulatory vibe from the performers. We are supposed to admire the accuracy of the character satirised by the performer, often aided by elaborate make up and costuming. It's a genre which has never really made laugh, the same characters got wheeled out every week with the same jokes. Harry Enfield has a lot to answer for. I even see this in Mike Leigh's early tv plays and films and I always found this sneering attitude in British comedy off-putting. Little Britain was part of that bit also almost a satire of it.