Artists and museums are often in the thick of free speech debates — think of Rudolph W. Giuliani’s battle with the Brooklyn Museum over a Virgin Mary artwork with elephant dung and more recently a fight over an exhibit that evoked Emmett Till’s mutilated corpse. Typically the art world holds its ground, emerging bruised but resolute.

But in two recent controversies, the protesters seem to be winning.

On Monday, the Guggenheim decided to pull three major works from a highly anticipated exhibition after pressure from animal-rights supporters and others over the show “Art and China After 1989: Theater of the World.” This, together with the Walker Art Center’s recent move to dismantle Sam Durant’s sculpture “Scaffold” in response to protests, has art leaders concerned that museums are setting worrisome precedents when threatened with organized pressure tactics.

“When an art institution cannot exercise its right for freedom of speech, that is tragic for a modern society,” the artist Ai Weiwei said in a telephone interview, referring to the Guggenheim’s decision. “Pressuring museums to pull down artwork shows a narrow understanding about not only animal rights but also human rights.”

The three works in the Guggenheim show, which opens Oct. 6, were created between 1993 and 2003 and were intended to symbolically depict oppression in China. One video, “Dogs That Cannot Touch Each Other,” shows four pairs of pit bulls on nonmotorized treadmills, trying to fight even as they struggle to touch. Another video, “A Case Study of Transference,” shows two pigs mating in front of an audience. And an installation — “Theater of the World,” a central work of the show — features hundreds of live crickets, lizards, beetles, snakes, and other insects and reptiles under an overhead lamp.