(FORTUNE Magazine) – "Disney thinks that they are so big we can't hurt them. But when you get too big for your britches, you've got problems coming." So says the Reverend Donald Wildmon, whose right-wing Christian group, the American Family Association, is backing Florida Baptists in a nationwide boycott of Walt Disney Co. and all its works. Bambi's been blackballed.

Why target a company that can be nauseatingly wholesome? Because Disney is producing entertainment--the movie Priest, e.g.--that AFA believes morally suspect. Worse, Disney has extended health benefits to the live-in partners of gay employees.

As Wildmon mobilizes his zealots, is Mickey ("Please don't mention Snow White living with the Seven Dwarfs") quaking in his oversize shoes? Hardly. Says spokesman John Dreyer with a shrug: "We regret that some people have taken offense at a health issue involving our employees, but we aren't going to change it."

Disney is not alone. At any given moment, dozens of U.S. companies are being snubbed by somebody. A few seem to be serial offenders. No sooner had Kmart called off Reverend Wildmon's dogs--his outfit was boycotting the retailer because its Waldenbooks division, now spun off, was selling Playboy--than AFL-CIO members got their noses out of joint because Kmart buys ads in the Detroit News, where a nasty strike is in progress.

Want to attract boycotters? Just get big enough and they'll find you. McDonald's was for years dogged by environmentalists who spread a false but devilishly persistent rumor that Big Macs contained beef from cows raised on land cleared from Latin American rain forests. Sighs McDonald's spokesman Chuck Ebeling: "With 10,000 locations nationwide, we're a lightning rod for the issue du jour."

The irony is that by the time a company gets big and visible enough to make irate consumers vote with their feet, it's too big for a boycott to affect it much. In October, a coalition of dairy farmers, consumer groups, and environmentalists in Wisconsin announced a boycott of Monsanto, claiming that its genetically engineered products are unsafe. Monsanto was unaware of the boycott until a reporter called the company's headquarters in St. Louis for a comment.

And what's the point in boycotting a product you never use anyway? Christian fundamentalists in Kansas and elsewhere are swearing off Coors beer, a seemingly odd choice given the highly conservative bent of the Coors family. But the brewer, like Disney, now buys health insurance for people whom boycott leader Fred Phelps Sr. refers to as "filthy fags." Odder still, Baptists don't seem to be the types who knock back a few cold ones after church. Coors spokesman Joe Fuentes allows as how the AFL-CIO boycott of the late Seventies, which included people like ironworkers and truck drivers, was a far greater blow. We bet it was.

--Anne B. Fisher