The World Council of Churches has appointed an American church leader, the Rev. Arie R. Brouwer, to direct the ecumenical organization's social action programs, including a controversial one on racism.

The Program to Combat Racism, which gives grants to groups in southern Africa, has provoked criticism in the United States that it aids Marxist revolutionary causes and has prompted the Salvation Army to withdraw from full participation in the council.

Brouwer, general secretary of the 375,000-member Reformed Church in America and a governing board member of the National Council of Churches, will begin his new job as a deputy general secretary of the World Council in September.

He will be the highest ranking American at the council's Geneva headquarters. More than 300 Protestant and Orthodox denominations hold membership in the council.

Brouwer said he is taking the post at a "sensitive" and controversial time for the council.

A doctrinal commission of the National Council of Churches, after 10 months of study, has reported it can't make a recommendation on the controversial application of a denomination serving homosexuals for membership in the council.

The council's Faith and Order Commission said that there is no clear answer in the council's constitution or statement of purpose and that each member denomination of the council should decide the issue on the basis of its own concept of the requirements of a church.

The council's governing board will discuss the membership application of the Metropolitan Community Churches at a meeting May 10 to 13 in San Francisco, but no vote on the issue is expected until a meeting next fall. The council includes 32 Protestant and Eastern Orthodox member denominations. Eighteen have submitted 200 pages of commentary on the question.

Three Episcopal bishops, including Bishop John T. Walker of Washington, have called on President Reagan to open a dialogue with the Nicaraguan government and to initiate a plan for massive assistance to victims of border strife in Central America.

The three also urged that the United States end any aid it is giving to right-wing forces against the government.

The appeal was made in a letter from Walker, Bishop George N. Hunt of Rhode Island and Bishop H. Coleman McGehee Jr. of Michigan after a trip to Nicaragua last month. The three met with church and government leaders there.

A $2 million lawsuit was filed Monday against two Mormon Church-owned companies by five former employes who say they were fired for failure to demonstrate worthiness to enter church temples.

The federal court suit, filed in Salt Lake City by the American Civil Liberties Union, contends the workers were interviewed by bishops of the Church of Jesus Christ of Latter-day Saints about their obedience to church teachings and the findings were reported to corporate personnel officers.

Bishops are required to ask such questions of all church members who seek to enter a Mormon temple.

"These questions were intimate, intensely personal and necessitated the answering of questions pertaining to sexual activities, moral cleanliness and purity," the complaint said.

Named as defendants in the suit were Beehive Clothing Mills, which makes special temple clothing worn by Mormons, and Deseret Gymnasium, a health club.

Church spokesman Don LeFevre said in a statement the church "has a policy of employing only worthy members of the church wherever such members are available." The policy is "in full compliance with federal and state laws," he said.

To enter a temple, where marriages and other sacred ceremonies are performed, church members must obtain a temple "recommend" from their local church leaders.

Requirements include giving 10 percent of gross income to the church, regular attendance at church meetings and avowal to the bishop that the member has followed the church's moral precepts, which include abstinence from alcohol, tobacco, coffee, tea, drugs, masturbation and sex outside of marriage.

The American Jewish Committee has urged the nation's governors to issue directives barring state officials from conducting state business in clubs that discriminate on the basis of race, religion or gender.

Committee president Maynard Wishner, stating that such a directive was issued in New York in 1980, said in letters to governors that states lacking similar regulations are in effect supporting discrimination.