A couple of years ago I was involved in a casual act of censorship. I was writing a piece for an arts organisation about contemporary performance and theories of art when somebody took exception to a quote that took a hatchet to the cliche of the tortured artist. “The artistic temperament is a disease that affects amateurs,” it went. “Artists of a large and wholesome vitality get rid of their art easily, as they breathe easily or perspire easily.” The line, it was firmly suggested, had to go.

The sentiment may have been provocative enough, but it was the speaker they found objectionable: GK Chesterton. Until then I knew Chesterton only as an author, a playwright and a critic; as a friend of George Bernard Shaw and Hilaire Belloc; as the creator of the Father Brown detective stories; and as a ready dispenser of aphorisms. "He is followed by controversy," came back one note. "Could we look at a more modern reference?"

That controversy, I found out, was the charge of anti-Semitism. In Chesterton's A Short History of England, from 1917, he described Edward I as "just and conscientious" when he expelled Jews from England in 1290, banishing people who were "as powerful as they are unpopular".

Chesterton’s biographers have long tried to temper the impression of him as an anti-Semite: an early and vociferous anti-Nazi, Chesterton “was never seriously anti-Semitic”, contended Michael Coren’s biography. But the damage could not be undone. For others, not only was the man eternally suspect, but even his thoughts on art had been contaminated. Anti-Semitism, whether avowed or suspected, is smoke that lingers. We took the quotation out.

This is one of the ways an artist’s reputation becomes and stays damaged, and, to adopt my redacted Chesterton maxim, how the art itself may be got rid of easily.

Broadly speaking, there are two theories about how artistic reputations are made: the “masterpiece” theory and the “art world” theory. If the work is good enough, goes the first, the artist’s reputation will always rise. Not so fast, says the second: if it finds an influential champion, a canny promotional campaign or a positively inclined interpretive community, and fits the prevailing ideology, then, as long as the art is good enough, a reputation will bloom.

How easy is it, then, for an artist’s reputation to be destroyed and for the art to become tarnished?

Something like that may have begun last week with Woody Allen. "What's your favourite Woody Allen movie?" began Dylan Farrow's open letter on a New York Times blog last weekend. "Before you answer, you should know: when I was seven years old, Woody Allen took me by the hand and led me into a dim, closet-like attic on the second floor of our house. He told me to lay on my stomach and play with my brother's electric train set. Then he sexually assaulted me."

Two decades since the allegation first appeared, Farrow’s letter has been taken as everything from a courageous statement to a sign of manipulation. Yet Farrow’s rhetorical device of opening and closing her account with the same question implicates the movie fan as an apologist for sexual assault. (Allen says her allegations are untrue and disgraceful.)

Take an undisputed example, that of Roman Polanski, who pleaded guilty to the statutory rape of a 13-year-old in 1977 and fled the United States before his sentencing. Can a person admire Chinatown or The Pianist without condoning a criminal?

These are hardly new questions. “How can we know the dancer from the dance?” WB Yeats asked in verse. In his case, how can we know poetry of such passion and humanism from a poet with uncomfortable interests in eugenics?

Is there such a thing as an innocent appreciation of TS Eliot, who not only entertained deeply hateful ideas in private but also let them seep into his writing? "Bolo's big black bastard queen / Was so obscene / She shocked the folk of Golders Green," Eliot wrote in his unpublished juvenilia. Then there is his Burbank with a Baedeker: Bleistein with a Cigar: "The rats are underneath the piles / The jew is underneath the lot. / Money in furs."

What our revulsion may expose is a certain prejudice we hold about art: that no matter the content, its makers should be beyond reproach, their moral conduct generally elevated, that they should share our better political convictions. The suggestion that they don’t smacks of personal betrayal, making us feel like guilty accomplices. Should we boycott their work, like ethical consumers? Should we deny and disprove it? Can we accept it?

We could take it back to Shakespeare, who was all things to all people. Speaking about "Bardolatry" last year, the academic Patrick Lonergan articulated a cognitive dissonance around staging Shakespeare's works: we prefer not to think of The Merchant of Venice as anti-Semitic or Othello as racist, shrugging off the fact that they were among the most popular plays staged in Nazi Germany. "It's part of our compulsion to see Shakespeare as a great man as well as a great writer," he said.

History has told us, though, and keeps telling us, that you can be a great artist and still have a lousy reputation. To accept that, without excusing it, makes the artist a bit more human, and allows the art to endure.

Fintan O’Toole is on leave