Why worry about antiwar views, anarcho-syndicalist politics and "Dump Bush Now!" placards when something serious is at stake -- like money?

The billionaire media mogul who happens to be New York Mayor Michael Bloomberg has decided that if antiwar protesters are to descend on his city by the hundreds of thousands for the Republican Convention, he may as well turn them into shoppers. So with just a hint of the sardonic, Hizzoner announced Tuesday a "Peaceful Political Activists" visitor program modeled after the one offered to Republican delegates.

Affix a "Peaceful Activist" button and a protester can claim a free glass of Montepulciano wine with dinner at La Prima Donna, rent a room at the boutique Dylan Hotel ($150 a night) and get dibs on discounted theater tickets. Perhaps "42nd Street" for the Quakers from Kansas and "Naked Boys Singing" for the South Beach set?

Cowboy-booted Republicans and nose-ringed demonstrators: Everyone's welcome. If this sounds like marketing to Royalists and the Jacobins who would like to behead them, that's pretty much the idea.

"New York is the place to get your message out, any message," Bloomberg says. "It's no fun to protest on an empty stomach. So you might want to try a restaurant." Hizzoner offers another example: "Or you might want to go shopping, maybe for another pair of sneakers for the march."

The program to welcome radicals comes backed by the full marketing power of the city's tourist wing, NYC & Co. Link to a Peaceful Political Activists home page through www.nycvisit.com, (we're not kidding), and find pages of events and every legally permitted demonstration. Stuck with time to kill between the Planned Parenthood demonstration and the Ukuleles for Sanity Concert? Take the "Bohemians and Beats of Greenwich Village" tour, walk by Stonewall Place (where the Gay Liberation Movement took militant wing), and end up with another tour: "Radical and Immigrant Heritage of the Lower East Side. Walk the streets where . . . socialists, anarchists and free-thinkers gathered."

Some of the lists prepared by the tourism agency are tailored to political tastes, but a certain ecumenicalism is assumed. The Museum of Sex offers the same $5 discount to Republicans and protesters.

Few protesters seemed amused. They note that their people are more likely to sleep on church floors, in hostels or on friends' couches than seek a $189 junior suite at the Avalon Hotel. Terrible cynics all, they assume Bloomberg wants to divert attention from his politically unpopular battle with United for Peace and Justice, the largest of the antiwar groups. Organizers want to end their Aug. 29 antiwar march -- which is expected to draw a quarter-million or so people -- in Central Park. But Bloomberg rejoins that so many feet would chew up the grass.

He has offered the organizers, take it or leave it, a spot along the West Side Highway. They've refused and called him "Mayor Meanie." Polls show about 80 percent of New Yorkers agree with the demonstrators.

Word about the discount plan no sooner leaks out on Tuesday than Beka Economopoulos of Code Pink: Women for Peace ("Not an organization but a phenomenon") dresses like a pink-swathed Statue of Liberty and stands outside the midtown headquarters of NYC & Co. "If the mayor wants to welcome us, then he should do more than get us tickets to a play," she shouts. "Give us a permit to rally, not a discounted dinner we can't afford."

Upstairs, Bloomberg stands flanked by two former mayors, David Dinkins and Ed Koch. Koch, a famous gourmand who is happiest when in conversation with almost anyone, plans to walk the floor of the Republican Convention handing out palm cards listing his 20 favorite restaurants. But he has a certain affection for protesters, too -- he argued for so long with so many when he was mayor.

"I remember the good old days when I'd come into City Hall around 7:30 in the morning and there would be two groups of protesters setting up their picket lines, and another group that had slept overnight in the park," Koch says. "I would walk over and say: 'Good morning, protesters!' "

"And they'd respond: 'Hello, Mayor!' "

New York Mayor Michael Bloomberg doesn't want protesters to go home empty-handed or empty-stomached.