The Justice Department has provoked a firestorm of protest from governors and local tax officials by entering a Supreme Court case in support of multinational companies contesting state corporate taxing powers.

"This is like a stick in the eye at the wrong time and wrong place," complained Alan Charnes, director of Colorado's Department of Revenues. The action "constitutes a serious encroachment by the federal government into prerogatives rightfully belonging to the states," said Victor Atiyeh, Oregon's Republican governor, in a letter to President Reagan.

At stake is a method used by a number of states to collect corporate income taxes based not just on a company's claim of profits within a given state, but on the basis of a proportional share of the worldwide business activities of the company and its affiliates.

The practice--used most extensively by California--has been attacked both by corporations, particularly foreign-based firms with U.S. affiliates, and by foreign governments, which contend that it interferes with international tax treaties and results in potential double taxation.

Estimates produced by advocates of the state taxing method and disputed by critics show that loss of the taxing power would cost the states $709.5 million in revenue, including $485 million in California, $25 million in Illinois, $75 million in New York, and $16 million in Idaho.

Many of the state officials contend that if the contested method of taxation is ruled illegal, corporations will be able to escape much of their liability through complex income shifts between affiliates and through accounting practices that are difficult to trace.

Citing specificially the practices of oil companies, Ken Cory, California comptroller, said: "When the various corporate divisions are in different jurisdictions which have different rates of taxation, there is an obvious opportunity to play a 'shell-and-pea' game in order to avoid taxes." He cited claims that Gulf Oil Corp. and Cities Service Co. had total sales of $33.7 million in Colorado in 1978, but reported no taxable income.

Until now, the public dispute over the tax issue has focused on pending legislation in both the House and Senate that would restrict the states' powers to use worldwide calculations. This past week, however, the conflict spread to the decision of the Justice Department to file an friend-of-the-court brief in support of a challenge to the use of the controversial taxing system by Illinois.

State officials contend that the Justice Department's entry into the case violates an administration commitment to remain neutral, for the moment, on the issue.

On May 2, 1981, James M. Medas, President Reagan's assistant for intergovernmental affairs, wrote Utah Gov. Scott M. Matheson, "The administration has, as yet, taken no official position on the state use of the unitary apportionment method for determining income of multistate and multinational corporations."

Stuart A. Smith, assistant to the U.S. solicitor general, said, however, that the Justice Department entered the case at the combined request of the Treasury, State and Commerce departments, as well as of the U.S. trade representative, who contend the tax is "an irritant to our foreign commerce."

Leslie Schreyer, the Treasury's deputy international tax counsel, argued that the entry in the court case does not violate any agreement with the states because the commitment to remain temporarily neutral only covered the legislative debate, not a pending court case.

Arguing that use of the worldwide system of calculating state tax liabilities in the case of foreign companies with U.S. affiliates violates federal constitutional powers over international treaties and foreign commerce, Schreyer said filing a friend-of-the-court brief opposing the tax is very different from "taking a position on legislation."

The Illinois case, however, focuses not just on the issue of taxing foreign-based firms with U.S. operations--a broad method used only by California--but also on taxation of U.S. companies with foreign affiliates. Schreyer said the goal of the government is to make sure the Supreme Court, which might well uphold the Illinois tax, will take note of the foreign-based-corporation question and leave that issue open for later consideration in separate litigation.

Echoing a repeated complaint from state officials that the Justice Department's action violates the president's claimed commitment to a new federalism, Theodore V. Spengler Jr., Idaho deputy attorney general, contended that the tax method under challenge in the case "is a fair and necessary part of our tax system when we are dealing with multinational corporations."