There is an illness that afflicts leading lights in the arts, an illness that you rarely encounter elsewhere. I call it "cultural paranoia". It involves major celebrities taking popular and populist stances, and then convincing themselves that they are being persecuted for doing so. Vanessa Redgrave suffered from this debilitating disease for several decades. And this week the celebrated actor Mark Rylance appeared to be showing symptoms.

Before going any further, I should stress that Rylance is one of the greatest actors of his generation, was a remarkable founding artistic director of Shakespeare's Globe, and is one of the most charismatic people that I have met.

But even he has fallen victim to cultural paranoia, and an extreme strain of the virus it turned out to be.

In an interview with The New Yorker, Mr Rylance finally explained why he surprisingly left the Globe three years ago. The principal reason, he says, is that he expressed "vocal opposition" to the Iraq war and, in his words, "it became more and more difficult for me to stay. They were afraid I would bring it [his views on the Iraq war] on stage."

Yes, one can see that the trustees of the Globe might not have stomached an anti-war stance either behind the scenes or on stage, and audiences, united in their support of Tony Blair, would have walked out in droves. No, wait a minute, that's not quite the case, is it? In fact, the whole of the arts world was against the war. You couldn't move for plays, pop songs, poems and novels opposing the invasion. I even sat through a politically charged opera production at Glyndebourne, with Mozart given a bit of anti-war attitude.

How could Rylance possibly have thought that an anti-war stance was putting his job in jeopardy? Indeed, it is more likely that had he been pro-war and mounted productions that were pro-war, he would have raised eyebrows among trustees and audiences – and then he would have been the only artistic director in Britain to take such a stand.

In opposing the war, Rylance was a member of a massive and united band of cultural thinkers, and, of course, a large swathe of the population. If he really did step down because of his stance on Iraq, then this was one of the most severe cases of cultural paranoia imaginable.

The second reason that Rylance gave in his interview is a more credible one for serious debate. He says that he does not accept that Shakespeare actually wrote the plays. His position on this is well known and has been well known for years. The board of the Globe would certainly have known it when it took him on. And it was quite indulgent to appoint him, knowing his radical views on the authorship of the plays. I suspect if he had applied to Bayreuth to run the annual Wagner festival, and said that he loved the music but wasn't sold on the notion that Herr Wagner actually composed it, his job interview would have been terminated on the spot.

But the Globe's indulgence on this matter was well rewarded by Rylance's artistic tenure. He was an inspired and inspiring figure, and while it was pretty strange for the man running Shakespeare's Globe to be the most high-profile doubter of Shakespeare's claims to authorship, his views on authorship never affected the Globe's productions, and his appointment was the right decision.

As for his fears on his anti-war stance, you didn't have to leave, Mark. This may come as a shock to you, but you were not alone.

You were a funny girl, Barbra

With the Chichester Festival Theatre reviving the musical Funny Girl, I am grateful to my colleague Rhoda Koenig for showing me the programme from the original 1964 Broadway production, which made a star of Barbra Streisand.

The programme says of Miss Streisand, pictured: "Her favourite flower is the gardenia, since it is the only scent that can never be captured. Her favourite day of the week is Tuesday, since she devotes part of each Tuesday throughout the year to stringing crystal beads which are sold in a Vermont general store. She knows how to make coffee ice cream and to fix her own hair. For more personal information, write to her mother."

Those were the days – when you were urged to write to a leading lady's mum. But my eye was caught by something even more remarkable in the programme. An article about the lack of black faces in Broadway audiences was headed: "Is there a Negro in the House?"

Sometimes the 1960s seem an awfully long time ago.

* The new chief executive of the 2008 Brighton Festival, which started this week, is Andrew Comben, an Australian who cut his teeth as national classical labels manager at Festival Records in Sydney. The chief executive of the South Bank Centre in London is an Australian, as is the chief executive of the Wales Millennium Centre in Cardiff, the general manager of Sadler's Wells, the managing director of English National Ballet, the director of the Royal Ballet School, and the manager of the London Philharmonic Orchestra.

The scheme set up by the former Culture Secretary Chris Smith to train the best young arts administrators in Britain, with a view to running top organisations, is preparing the next generation. But it should add a new module to the course. I would suggest that every student is allowed to have a period of secondment to Australia to study how it's done there. They've clearly got something we haven't.