When the law was introduced in 2009, officials claimed that they were just adhering to the constitutional requirement that one exist — and that they had written it to be essentially unenforceable. (The law replaced a measure outlawing only blasphemy against Christianity, not other faiths. It was found to be discriminatory.)

But Eoin Daly, a lecturer in constitutional law at the National University of Ireland, Galway, said that it was possible prosecution might occur in an “egregious case,” and that the law had a “chilling effect” as long as it stayed on the books.

Michael Nugent, a spokesman for the advocacy group Atheism Ireland, welcomed the referendum, saying that even in the absence of prosecutions the law was causing real damage to freedom of expression in Ireland, and to the country’s reputation abroad.

Mr. Nugent said he was aware of cases in which news organizations had “self-censored” to avoid the potential cost of a blasphemy complaint, however vexatious.

And internationally, he said, the wording of Ireland’s law has been taken up by Islamic states seeking to justify their own blasphemy laws.

“We became a Western poster boy for Islamic states and their oppressive practices,” Mr. Nugent said. “It’s never a good look when Pakistan, where people are killed for blasphemy, is speaking approvingly of your laws.”

In announcing the referendum on Tuesday, Ireland’s justice minister, Charles Flanagan, also pointed to countries where blasphemy was punishable by death.