No Cabinet appointment better symbolizes the change in government the Reagan administration is likely to bring to Washington than the selection of James G. Watt to head the Interior Department.

President-elect Ronald Reagan campaigned against evironmental extremists and promised his administration would bring a change in philosophy. In Watt, he appears to have found the ideological soulmate, a man who yesterday described many of the department's policies as "oppressive."

Watt's philosophy has made his cabinet appointment extremely controversial, and yesterday's announcement of his selection brought on immediate outcry from environmental groups.

For the past three years, Watt has fought for the government from his post as president of the Mountain States Legal Foundation in Denver. Yesterday he made clear he believes the government has an obligation to develop the resources on public lands, rather than protecting the land from developers.

"We cannot afford to lock up from utilization our resources for one specific purpose," he said. "The art of managing the department will be to bring a balance to the utilization of our resources."

Watt has complained that environmentalists are blocking the "orderly development" of energy in the West and is said to believe that his approach is the healthier policy for protecting western land.

Asked yesterday to explain how he defined environmental extremists, Watt said, "Extremists are those who would deny economic development" on public lands.

"The entire environmental movement is disturbed," said John McComb of the Sierra Club. "He's very much in favor of free and virtually unlimited access by private economic interests to public land," said Pete Lafen, a spokesman for Friends of the Earth. "We're opposed to his nomination and believe it should be rejected by the Senate." Environmental groups met last week to organize their opposition to him, although no date has been set for his comfirmation hearings before the Senate Energy and Natural Resources Committee.

Much of the discussion in those hearings is likely to center on the activities of the Mountain States Legal Foundation, which receives financial support from beermaker Joseph Coors, a political conservative.

The foundation has argued in court that the Interior Department's Bureau of Land Management does not have the right to restrict grazing on land environmentalists claim is overgrazed; that Colorado public utilities are not social welfare agencies and should not be allowed to give rate breaks to the handicapped, the elderly or the poor; that the Environmental Protection Agency should not be allowed to require the state of Colorado to set auto emissions standards; that the deadline for approving the Equal Rights Amendment should not be extended, and that an Oklahoma rancher fined $500 for spilling oil into a creek should not have to pay because he reported the violation to the government.

Watt also said yesterday he has been "part of the Sagebrush Rebellion," a movement in the West to force the federal government to turn over control of its land to the states. But Watt said the solution "is good management of the Department of the Interior that would put aside the oppressive policies" of the federal government."

Watt, 42, was born in Wyoming and was graduated from the University of Wyoming and its law school. From 1969 to 1975 he worked at the Interior Department, first as deputy secretary for water and power resources, then as chief of the Bureau of Outdoor Recreation. In 1975, he was appointed to the old Federal Power Commission.