Some of President Reagan's oldest supporters on the political and ideological right are upset with his response to the hijacking of TWA Flight 847. Many conservatives have demanded immediate retaliation, and one alliance of prominent conservatives wants Secretary of State George P. Shultz to resign.

A sharp attack on Reagan's policies was issued this week by the new Coalition for Action Against Terrorism, which includes the Moral Majority, Paul M. Weyrich's Free Congress Research and Education Foundation, direct-mail fund-raiser Richard A. Viguerie and the Conservative Caucus.

"In any other democratic country in the Western alliance that had hostages being held by an alien group, the equivalent of our American secretary of state would immediately offer his resignation," said Ronald S. Godwin, executive director of the Moral Majority. "This is the very least Mr. Shultz should do."

According to Weyrich, "Shultz is a master of taking a hard line rhetorically and a soft line in policy. We ought to be pounding terrorist camps inside Lebanon." Specifically, the coalition called for "preemptive and retaliatory strikes against terrorist bases and training camps."

Unlike Weyrich and Godwin, Norman Podhoretz, editor of the neoconservative monthly magazine Commentary, went directly after the president.

"Reagan, no less than Carter," Podhoretz wrote in a Los Angeles Times column, "is permitting the United States to undergo a protracted humiliation."

Podhoretz specifically attacked Reagan's reluctance to retaliate for fear of killing innocent civilians, accusing the president of adopting an argument used by "academic apologists for terrorism."

Other conservatives expressed more support for the president.

Robert Heckman, chairman of the Fund for a Conservative Majority, praised Reagan for "making it clear that we are not negotiating" over the hostages. Heckman, like many other conservatives, argued that the United States must retaliate when the crisis ends.

He said his main dispute with the administration centers on its argument that retaliation be restricted to those who participate in terrorist activities. Heckman said government leaders and others who "condone" terrorism should be included.

Gary Jarmin, chief lobbyist for Christian Voice, which issues evaluations on the "morality" of votes by members of Congress, said: "We find the president so far has acted properly, and we are behind him. However, we must find a way to make the terrorists pay a price."

Rep. Newt Gingrich (R-Ga.), a founder of the Conservative Opportunity Society, said Reagan has the "correct instincts," but the administration should have maintained a low public profile to prevent any impression that U.S. leaders were shaken by the hostage-taking.

John M. Fisher, president of the American Security Council, said that "it's easy to sit" in a Washington suburb "and criticize the president, but in general, I think [the administration's reaction to the hostage-taking] has been okay." Fisher also called for retaliation.

James Phillips, Middle East analyst at the Heritage Foundation, was highly critical of the administration, saying that the hostages are "payment for the failure to respond" in the past, including inaction after the suicide bombing of the U.S. Marine headquarters compound at Beirut airport in October 1983.

Phillips, generally complimentary about Shultz, said that Defense Department officials have been more reluctant than State Department leaders to commit the country to a hard-line retaliatory posture.

One of Reagan's harshest critics has been the The Wall Street Journal. Two days after the hostages were taken, The Journal suggested "that President Reagan order military strikes against Syrian military installations inside Lebanon."

Four days later, when Reagan had pointedly not taken military action, a Journal editorial, headlined "Jimmy Reagan," charged that the president had adopted policies amounting to "engraved invitations to terrorists throughout the world."

This week's edition of the conservative weekly Human Events carried this front-page headline: "Hawks Concerned About Reagan's Foreign Policy."

The article said: "What conservatives see is an attitude -- underscored by the hostage situation -- in which the administration appears especially eager to accommodate its enemies, whether they are Soviet goons or Islamic terrorists."