THE FUROR over Saudi Arabia's protests against the showing of "Death of a Princess" by the Public Broadcasting Service is both more and less that it is made out to be. The Saudi protest, and those of its oil partner, the Mobil Corporation, along with some of the heavier interventions of the State Department and certain members of Congress, make it essential that the show be seen on schedule Monday evening. None of this should even be negotiable. The outcry, of course, makes it inevitable that an extra large audience will tune in. The incident is more than it appears to be because, with the power that Saudi oil and financial resources confer, Saudi displeasure can have costly consequences. When the same film was shown in Britian, for instance, the Saudis expelled the British ambassador -- notwithstanding an official apology for the film -- and undertook a line of economic sanctions whose end, to British dismay, is not yet in sight.

The incident is -- so far -- less than it appears to be, however, because the official Saudi protests against the American showing have, by contrast, been phrased in very hedged terms. The Saudis have criticized a "docu-drama," which they find replete with "false episodes, serious inaccuracies and outright prejudice." But on the record at least, they have not asked PBS and other news media "determine for themselves what the fictitious items and distortions are and . . . not report them to the American public as fact" -- to which the immediate response must be: how else can this be done except by seeing the show? The Saudis would also have liked a statement by the U.S. government characterizing the film as "distorted and inaccurate." The State Department declined to go that far. But in a way this would have been preferable to its direct approach to PBS with a request that PBS assure its viewers "a full and balanced presentation." PBS intends to do that anyway, at least by their earliest public statements, by conducting a discussion of the show on the air after it is run, and it would have been well for the State Department to have left it alone in the first place.

The Saudis indicated that, though they are affronted by the show, and perhaps worried by the way it will play into an internal debate of their own, they did not wish to make the incident a test of their relationship with the United States. Perhaps they feel that American-Saudi relations are already under enough strain.

By contrast, Mobile in its ad has raised the stakes, declaring that "the best interest of the United States" is involved, and urges PBS to "review its decision to run this film." If Americans decline to delete television programs because foreign governments object to them, they will certainly decline when American corporations object, even corporations like Mobil, which heavily supports PBS. (We note, by the way, that it seems a grotesque "defense" of the First Admendment for a court in Texas to have ordered the film to be shown.) Perhaps Mobil is out in front acting for the Saudis, making the threats the retiring Saudis prefer not to be heard uttering in public themselves. If that is so, we are all better off replying just to the Saudis and telling them -- as now PBS is -- that the show is receiving precisely the critical dissection the Saudis have said it deserves and that good journalistic practice would have brought this about anyway, and that the show will go on.