There have always been people who have found reasons to take offence. In moments of high tension, you have always been able to find people who are offended if you will not give them reasons to take offence. But the heresy hunters who took offence at the feeble joke Andrew Neil used to introduce the BBC's This Week are a novelty. They belong to a new breed of digitally enabled puritan the internet has unleashed.

In case you missed it, Neil began his political show by mocking Gordon Brown for failing to answer an inane request to name his favourite biscuit. He then turned to his guests, Diane Abbot, who is black, and Michael Portillo, who is not, and said: "And here we have our very own chocolate HobNob and custard cream of late-night telly."

A few viewers complained, not because they thought that if the imperious Ms Abbott were a biscuit she would be a Bourbon, but because the accusation stirred in their ever-suspicious minds that Neil was a racist. Instead of telling them not to be silly, the BBC pulled the programme from its iPlayer. Bewildered observers pointed out that the wife of John Pienaar, Radio 5's political correspondent, was responsible for the allegedly insulting script. As her husband is also black, she seemed an unlikely bigot.

The BBC was cowardly, but perhaps understood better than its critics how the net is reducing the cost of complaining to zero and allowing waves of outrage to crash through cyberspace. A generation ago, protest was hard work. Organising a demonstration involved negotiating with the police, agreeing a reasonably coherent programme with allies, hiring coaches and appointing stewards. Even running a write-in campaign necessitated persuading people to take the time to draft letters and post them. A few hundred complaints was an impressive total in the circumstances.

Now Facebook groups and trending topics on Twitter can, if they ignite, produce mass protests from nowhere. Links to the relevant regulators' websites and pre-written objections to insert in them are also to hand. And the truly enraged can then move on and join "flash mobs" which organise protests online in hours or days rather than wait weeks for old-fashioned demonstrations.

I have known for years that the Daily Mail hired homophobes as columnists – no, really, I have – but others were shocked beyond measure by the discovery that Jan Moir could use the death of Stephen Gately as a reason to sneer at gay marriages. About 22,000 protested to the Press Complaints Commission. The number of objections to the equally obnoxious baiting of an old man by Jonathan Ross and Russell Brand on Radio 2 bettered that total and hit 37,000. When cries of "shut them up" and "shout them down" are roaring across the web, I see why the BBC was keen to stop the HobNob affair in case it went viral.

Before I go any further, I must acknowledge that the net is helping the campaign to prevent the English judiciary silencing scientists who criticise quacks, and that bloggers and tweeters blew apart our wretched legal profession's attempt to ban the Guardian and Parliament from discussing what the toxic waste Trafigura dumped off the Ivory Coast did to Africans.

Despite the good the net brings, however, you can always rely on people who willingly join a mob to set their own home on fire eventually. The air is thick with the smell of burning principles and not only because the same people who want freedom of speech for Parliament want to silence Jan Moir.

The ease of net communication explains why so much abuse appears in comments boxes. But it also undermines the authenticity of many mass protests. The targets feel as if they are on the receiving end of genuine popular feeling, when typically the anger directed against them is shallow and transient. In the British Journalism Review, to take a conclusive example, media studies academics Suzanne Franks and Jean Seaton examined the apparently heartfelt protests against the BBC's refusal to broadcast an appeal for the victims of the war in Gaza.

At the height of the controversy in January, the BBC Trust had logged more than 22,000 complaints from campaigners who seemed desperate to do what ever they could to get aid to the afflicted. The alleged concern of almost half of them was phoney. At precisely that moment, the number of true altruists who had put their hands in their pockets and contributed to the appeal stood at a mere 13,000.

The largely conservative campaign against Jonathan Ross was equally confused. Tories who pose as plain-speaking Englishmen and women and affect to despise political correctness could not accept an apology for a repellent but isolated breakdown in standards but wanted to destroy the careers of everyone who had transgressed the speech codes of the right. Last week, the Telegraph was running disingenuous comment pieces condemning the BBC for imposing rigid controls on its comedians. After the battering it had received, what did the Telegraph expect it to do?

Earlier this month, meanwhile, when Twitter heaved with protests against Jan Moir, apparent liberals matched conservatives and forgot every liberal principle they knew. Marks & Spencer responded to their protests by pulling its advertising from the Mail.

The fashionable media model is for newspapers to give their contents away free on the web and rely on advertisers for money, a strategy that will inevitably give commercial interests the muscle to be censors. Instead of wondering what might happen to investigations into corporate tax avoidance in future, bloggers welcomed advertisers' attempts to dictate an editorial line by citing the boycott as "a brilliant example of how reader power in the new media age can hurt newspapers".

A mob fighting a good cause is still a mob. To fight back, you need to remember that although the internet age is hugely expanding the number of complaints, the old rules still apply. Whether you are the owner of a tiny blog or the editor of a national newspaper, if someone points out an incorrect fact, you correct it; if someone challenges an argument, you argue back; and if someone says that you must think what they think, you ignore them.