Whenever I visit my grandmother she usually asks me to drop into the local shop, on a Saturday, to pick her up a copy of the Daily Mail. I've tried to persuade her to read something else – to broaden her horizons as it were – but she flatly refuses. I'm learning that steadfastly refusing to try new things is one of the privileges that comes with getting older.

What I don't bank on is having to face the same argument again in the shop – though this time I'm the one being harangued. For every time I drop in to buy my grandmother her paper, the shop assistant chooses to pass comment about it. "Nice to see someone buying a decent paper," she will say ingratiatingly if she spots me carrying the Guardian. If, on the other hand, my gran's copy of the Daily Mail is nestled under my arm, she will hold court on the "bigots" who've already been in that morning to pick up theirs.

For the most part I agree with the sentiments – sentiments I didn't ask for but which are unloaded on me free-of-charge. Still, it feels oddly grating to be lectured unprompted like this about what I did or didn't ought to be reading – especially as I rarely bother opening the Daily Mail in the first place. It isn't a big deal. However it does make me want to tell the person sermonizing to bog off – or perhaps to stop making snap judgements about people based on the newspapers they buy.

The news that Virgin Trains has decided to stop selling the Daily Mail on its West Coast trains reminded me of this. There is something hectoring and annoying about it yet it isn't – as some have suggested – a big deal in isolation. It certainly isn't an act of censorship.

After reviewing products sold on its trains, Virgin has decided that the Daily Mail is "not compatible with the VT brand and our beliefs". Concern had apparently been expressed by staff working on Virgin Trains about the newspaper's stance on things like immigration and gay rights.

The move has been decried as an attack on free speech by the Daily Mail and its political allies. "We are heading in a worrying direction. Banning things because you don't like them solves nothing," tweeted the former leader of UKIP Nigel Farage in response to the story.

Farage is for the most part wrong of course. Nothing is being 'banned'. For one thing, the reader of the newspaper in question can simply buy it elsewhere – the Daily Mail is sold in practically every newsagent in the country. If you believe, as free marketeers like Nigel Farage presumably do, in an individual's right to run a business as he or she sees fit then it doesn't seem unreasonable to allow the business to decide for itself whether it stocks a particular newspaper.

You might also notice that many of those who previously insisted on a businessperson's right to, say, refuse to bake a cake for a gay couple are all of a sudden up in arms about private belief mixing with commercial activity. A boss can turn someone away because of their sexuality, but woe betide that company if it fails to stock a newspaper which, funnily enough, comes down on the same side as these free speech warriors on a host of social and political questions.

Of course, it is important to recognise that the 'mob' can censor too, and many of the arguments in favour of restricting the sale of the Daily Mail on Virgin Trains are disingenuous. I've been reminded in the past 24 hours of some the sophistry Stalinist governments once used to effectively shut hostile newspapers, usually by encouraging state-run paper factories to refuse to supply paper. The point is, it doesn't have to be a direct attack on free speech for the result to effectively be the same.

Especially sinister are the increasingly voluble arguments equating the written word with physical violence. Despite its ubiquity among people like Nigel Farage, the word 'snowflake' is an appropriate moniker for someone who believes that merely sitting in the same train carriage as the Daily Mail somehow breaches their human rights.

Perhaps most dispiriting of all is the feeling that this kind of thing won't further decent causes in the long run. It may not constitute censorship, but as the mania for banning things – or at least for encouraging others to ban things - gains ground it will gradually lay the foundations for worse demagogues than Paul Dacre. Not because of any 'backlash' – a line of thought (I won't say 'train') which usually segues into some form of victim blaming – but because we will have forgotten how to argue back.

Performative bans and denunciations rarely change minds – as I'm learning every time I visit the shop on behalf of my gran. It seems particularly cavalier to champion large private corporations – hardly the historical bastions of radical causes – to act as our fledgling political commissars.