Fewer elk, for instance, means less food for grizzlies and wolves. It means less carrion for ravens and coyotes. Livestock also affect wildlife through social displacement. Elk, for instance, will avoid area actively being grazed by cows. This could preclude use of the best habitat by these native species all to benefit an exotic species.
Livestock are also one of the major vectors for diseases transmitted to native wildlife.
From mad cow disease that causes deer and elk brains to turn to mush to pink eye that causes bighorns to go blind, the transmission of disease from domestic animals to wild animals often has disasterous consequences. Because livestock are vulnerable to predators, ranchers have essentially eliminated predators from the West. They are the major reason why grizzlies and wolves are restricted to a few small relict populations. Pest control in the name of the livestock industry has devastated prairie dogs and their associated wildlife species. To appease the livestock industry, government agencies regularly spray to kill grasshoppers directly reducing the food available for many species from gulls to ground squirrels all of who prey upon grasshoppers.