Heard the one about a Huguenot, a Jew, an Irishman and a Bangladeshi? The metropolitan chatterati are in a right state over a new play at the National Theatre in London – Richard Bean's England People Very Nice – because it deals with the vexed issues of race, multiculturalism and immigration. If it were just some trendy types contorting themselves into their predictably anguished, politically correct positions, it would be merely amusing.

But today, Nicholas Hytner, the National's artistic director, has agreed to meet a delegation from Equal Platform, headed by Hussain Ismail, who says the play is "offensive stereotyping", "a personal attack" and "racist". The play, charting immigration over several centuries in London's East End, is riotously funny and cleverly devised, and deploys all sorts of theatrical and literary tropes – exaggeration, irony, play within a play – to tell its story.

One does assume a reasonable level of sophistication among National audiences, but clearly poking fun at ethnic stereotypes, such as suggesting that French Huguenots smelled of garlic, or the Irish are too fecund for their own good, or that young British Asians' patois sounds ridiculous, has been taken by Mr Ismail as a literal statement of the National's view of immigrants. As a playwright friend said to me, the play may just be too funny for its own good.

There isn't a scintilla of racism in it and I wouldn't dream of defending it if there were. Rather, it is a heartfelt argument for assimilation (or "having sex with the locals", as the relentlessly humourless Mr Ismail has it) and – the play's serious purpose, cogently argued – the danger of some radicalised Muslims wishing to remain separate from British society, which they regard as the infidel.

That worries me, but what worries me far more is this campaign against the National, which is nothing less than an attack on freedom of speech. Mr Ismail, who describes himself as a theatre worker of Bangladeshi origin but who sounds like Dave Spart's long-lost cousin the minute he opens his mouth, has demanded that Mr Bean "be brought to account" at a public meeting (public lynching, anyone?), that the National's website carries an apology and that each copy of the play's programme includes a rebuttal by the offended parties. It would be funny if it weren't so tragically misguided.

I speak as the daughter of Irish immigrants (one of six children – hey, I'm a stereotype, too) who faced signs saying "No blacks, no Irish" when they tried to rent rooms or applied for jobs in post-war Britain. But over time, that offensive nonsense abated and they settled in London, enjoying the far greater opportunities available here than in Ireland – or "home", as they called it to their dying day, because it is possible to retain a sense of self while being adopted into another culture. They believed in a united Ireland, but were appalled when the UK was under attack from paramilitaries – and my dad would walk out of any pub where a collection went up "for the lads".

I applaud Mr Hytner for staging an important play that celebrates our rich multicultural past, present and future. But I am appalled that he has agreed to meet this delegation. So, I say to him: by all means explain to these sadly deluded people what the play is really about, but don't you dare apologise.

Veronica Lee is a writer and critic