^^^If "'Allo 'Allo" took the mickey out of anyone, it was the British. (e.g. the ridiculous RAF officers and the spy, posing as a French policeman, who couldn't speak decent French).
Johnny Speight and Warren Mitchell both went out of their way to explain that "Till Death Us Do Part" was an attack upon racist (and xenophobic) views. [In a similar vein, much of the humour in "Rising Damp" was based upon mocking Rigsby's racist (or, at best, uninformed) views about people from Africa].
It has been widely suggested that the only reason that "It Ain't Half Hot Mum" isn't repeated on TV is because Michael Bate 'blacked up' for his part. Jimmy Perry (who regarded the series as the finest writing by the Croft & Perry partnership) has since explained that, at the time, there were simply no Asian actors available to play the part.
However "The Black and White Minstrel Show" did, at the very least, risk perpetuating images of black people that were far from positive. Perhaps BBC executives started to see it as an anachronism when it became the the corporation's first programme to be shown in colour?
Even so, I have to say that (at the time) I never even saw it as representing black people. I simply saw it as performers dressing up in traditional costumes (in the same way that pierrot artists might do). Similarly, when I had a golliw0g as a child, I never thought of it as a person (of any race or colour). I simply saw it in the same way that a child today might see a Smurf soft toy.