The following ought to be taken with a large pinch of salt, but I think it has a nugget of truth in it.
There will always in any society be gossips and people who go around "speaking things which they ought not", as Webster offers us in his example of a quotation about the word busybody. People who give a public airing to other people's private matters idly or for their own benefit are never going to be well liked, at least by the people whose dirty laundry they're displaying to the world. This private, social meaning of the word busybody is simple enough to understand and presumably universal.
But it also seems to me that there's another way in which we use the word busybody or its synonyms in the modern world which casts some light on the experience of living in a modern, liberal democracy. One of the most notable features of modern life in the West is the remarkably large private sphere that each individual has for "life, liberty, and the pursuit of happiness". Our societies are based on - or so we believe - the ethics of the self-reliant bourgeoisie, who ask for everyone to stay out of their way so that they can get on with pursuing happiness and wealth on their own.
The flipside of his self-reliance is a loneliness which comes from believing he has only himself and immediate family to rely upon, in contrast to pre-capitalist forms of social organization where there was greater social hierarchy but also greater acknowledged social responsibility of aristocrats for their peasants, of peasants for the rest of the village, and so on. While we certainly shouldn't idealize pre-capitalist forms of social organization, the relative alienation from other people which accompanies the dog-eat-dog structure of a capitalist society is, I would think, self-evident. The focus of capitalist society on the personal rather than the communal tends to lead not only to avarice but also to a mistrust of others, who presumably have their own schemes for getting by and getting rich and will step all over you to get their way.
From this springs the distinctively bourgeois meaning of the word busybody, typically applied to public officials like policemen and politicians. Bourgeois ideology and the bourgeois way of life has difficulty relating to the public sphere of governments and public service, as it is blind to the need for communal solidarity and self-sacrifice in binding any society together. We don't live in an entirely capitalist world, or a world entirely ruled by the dog-eat-dog ethos of the marketplace, because such a world would never last; we need people of talent and intelligence who are willing to eschew the large rewards they could accrue in the marketplace to run for elected office, run our social services, and staff the police.
But however much a capitalist society relies on these things being done, its ideology cannot explain them or relate to them - and so there is always the tendency among those involved in the private pursuit of their own wealth and happiness to view the motives of public officials as being identical to their own.
Bourgeois ideology is less troubled if it can be demonstrated that public officials in fact only take the trouble to carry out their duties because of the private gains for themselves involved in doing so - hence a popular phrase in the United Kingdom runs "anyone who wants to be a policeman shouldn't be allowed to be one", because their desire obviously stems from the desire to gain from their position. The cynicism of this phrase - its dismissal of the idea that anyone could be inspired by a genuine idea of public service - is obvious. They want only to benefit from their position, using the excuse of public responsibility to pry into the private business of others for their own gain; they're a busybody.
We find the same sentiment applied to others who interest themselves in public matters - politicians, for instance, who are frequently suspected of not only wanting to enrich themselves but also of meddling in the lives of citizens with their schemes, no matter how well-intentioned. Campaigners for public morality, public health, and environmentalism are likely to sustain the same criticism of unduly intruding into personal privacy and autonomy for their own gain (even if it is purely psychological: to make themselves feel better). The private sphere is the most precious thing there is to modern citizens, and they are hyper-vigilant when faced with those who want to intrude into it. The exact word "busybody" might not be used in its defence, but the meaning is there. It is hard to imagine any society not privileged with so large a private sphere and so great a degree of social freedom expressing quite the same sentiment.