In the case of Omaechevarria v. State of Idaho in 1917, the U.S Supreme Court ruled on a dispute involving grazing rights on federal land. The plaintiff, Domingo Omaechevarria, was a sheep rancher who had been convicted under an Idaho state law that prohibited allowing livestock to graze on public lands without permission from the owner or custodian. He argued that his conviction violated his constitutional right to equal protection because cattle ranchers were not similarly prosecuted and also claimed that only Congress could regulate use of federal lands. The Supreme Court upheld Omaechevarria's conviction by ruling against him. It held that while it is true Congress has exclusive authority over federal property, this does not prevent states from exercising their police powers in ways which might incidentally affect those properties. Furthermore, they found no violation of equal protection as there was no evidence showing unequal application of law between sheep and cattle ranchers; rather it reflected different impacts each type had on vegetation due to differences in feeding habits.

In the dissenting opinion for Omaechevarria v. State of Idaho, it was argued that the law in question, which prohibited sheep herding on open range land if it caused damage to cattle grazing lands, unfairly favored one industry over another without a rational basis. The justice contended that this legislation violated equal protection under the Fourteenth Amendment because there was no reasonable ground for distinguishing between harm done by sheep and harm done by other animals such as horses or swine. Furthermore, he pointed out that all livestock could potentially cause similar damage to public grazing lands and therefore should be treated equally under the law. He also disagreed with majority's interpretation of police power in this case; while acknowledging states' rights to enact laws protecting public health and safety, he believed these powers were being used unjustly here to discriminate against certain types of livestock owners.