THE CLASH between New York Mayor Rudolph Giuliani and the Brooklyn Museum of Art over an exhibit that includes a dung-smeared collage of the Virgin Mary has a familiar quality. But the issues posed by public funding of "shock" art cannot be evaded. The mayor has said he will cut off all public funding from the museum -- some $7 million in subsidies, nearly a third of its budget -- unless it cancels a scheduled show called "Sensation! Young British Artists From the Saatchi Collection."

The show has the explicit purpose of being as provocative as possible. It succeeded handsomely in London and Berlin (though protesters there focused less on desecration of the Virgin Mary and more on such pieces as artist Damien Hirst's sliced carcasses in formaldehyde). In New York, Mr. Giuliani is provoked, all right, and so are a number of other people and organizations, including John Cardinal O'Connor and the Catholic League for Religious and Human Rights. Plenty of non-Catholics object, too.

Unlike these groups, though, Mr. Giuliani has chosen an ill-advised and probably unworkable way of venting his outrage. It's reasonable to question the museum's judgment in mounting such a show and yet to question the mayor's assault as well. His attack may not make it through the political process: Not he but City Council President Peter Vallone has final say over the budget, and Mr. Vallone has expressed outrage but objected to stopping the museum's checks.

We doubt that what the mayor threatens is outright unconstitutional -- the recent court record on public funding of expression, as opposed to expression itself, is murky. Legal or illegal, the better solution is to respect the museum's basic autonomy in its choice of exhibits and to permit those so minded to see the show.