While this is very nearly true despite my disagreement with the framing, there is an important distinction between offensive graphical content, like porn or violence, and offensive intellectual content, like racism or sexism. That is what changed - they previously attempted to make sure you were not exposed to imagery they didn't like, now they attempt to make sure you're not exposed to ideas they don't like.
That's not a distinction the BBC's editorial team has ever used. Historically it has bleeped words ranging from "fuck" to "Coca Cola" and discouraged talking about ideas deemed inappropriate for the audience like most verbal references to sex before 9pm. People who range from neutral to outspokenly in favour of that sort of censorship are, however, liable to be enraged by the renaming of a dog in Dambusters (the original naming had far less expressive purpose than the average expletive!).
The shift is clearly more of one from ideas that certain groups consider to be of no value ("vulgarity") to stuff which they consider to be at least relatively valuable "the treatment of casual racism as completely normal behaviour which shouldn't provoke any reaction and might actually be funny, because that's just how things were in the good old days".
Bleeping is another important distinction. It lets you know something was there, and leaves you with a pretty good idea of what it was, preserving the message without preserving the shock value. Cutting bits out entirely and leaving nothing in their place is censorship in the sense that the article is trying to evoke, in a way that bleeping isn't.
You're cherry picking bleeping from that post. There is no type of censorship the BBC and TV regulators have not engaged in throughout its history. Bleeping, cutting away, using euphemistic terms, selective editing, not permitting discussions at all, demanding artists record versions with words like "cherry cola" seamlessly inserted in place of the inappropriate "Coca cola" for broadcast, banning other songs for openly political reasons or just because a senior exec hated jazz, excising material that might be subject to libel action, avoiding giving representation to political views sufficiently far outside the Overton Window, censuring presenters for expressing their own political opinions, even relatively unusual ones like requiring Sinn Fein politicians' statements to be revoiced by an actor just in case the original vocal inflections carried any coded messages to terrorists.
The type of edits engaged in have not changed at all, merely the subject matter, which has always had an ideas and politics and offence-based dimension but now takes a somewhat less conservative stance on what is and isn't appropriate. Arguing a threshold has been crossed because casual racism has replaced other things like homosexuality or mocking royalty on the long list of reasons the BBC might deem a sequence inappropriate for broadcast in certain contexts isn't a principled preference for freedom of artistic expression or the circulation of political ideas, it's a culture warrior's opposition to antiracism specifically .
One minor nit: the Sinn Fein revoicing was done by the BBC, but not for that reason. The government had required them not to broadcast SF and IRA 'propaganda' and the revoicing was a way to get around that ban. Thatcher was, apparently, livid.
