The Moral Majority is growing in public recognition, but half the American public still has not heard of it. The other half is enormously divided over this organization that terms itself the voice of the religious right.

Of those who say they know of it, 43 percent say they disapprove of its positions on most issues, 37 percent say they approve and the rest have no opinion.

Few Americans, however, seem to want to two-year-old group, based in Lynchburg, Va., to gain in power. Again dealing with those who know of its existence, only one in five wants the Moral Majority to exert more influence over American life than it does now, and more than half say its influence should be reduced.

These are among the findings of a Washington Post-ABC News poll dealing with the Moral Majority, the group led by the Rev. Jerry Falwell which claims to have registered 2.5 million fundamentalist voters last year.

The poll suggests that a substantial number of people who say they know of the Moral Majority and who express approval of its goals may in reality be unfamiliar with those goals. For example, almost half those who told Post-ABC interviewers that they generally approve the position "the Moral Majority takes on most issues" also said that they approve the Equal Rights Amendment, which the Moral Majority opposes.

Furthermore, while the Moral Majority decries homosexuality, four in 10 of those who say they approve the goals of the Moral Majority also say they believe "homosexuals and lesbians" should be allowed to teach in public schools, and that homosexual relations between consenting adults should be legal.

Nonetheless, the poll provides evidence that the Moral Majority is growing in recognition, in that a Gallup poll last December had only 40 percent saying they knew of it. In addition, the new survey provides a revealing glimpse of the group's staunchest supporters, and the deep-seated national concerns it has capitalized on.

Among those polled, three-fourths of the Moral Majority's strongest supporters voted for Ronald Reagan, and, like Reagan, consider themselves conservatives. They are far more religious than the rest of the country, have less formal education, and tend to live in suburbs and small towns in the South, Midwest and West. They are more likely to be blue-collar workers than professionals, Republicans than Democrats.

The greatest opposition to the Moral Majority comes from liberal Democrats, Catholics, college graduates, big-city dwellers and those who live in the Northeast. There is little difference in age, sex or income levels between those who support or oppose the group.

The poll also indicates widespread support among the public at large for many -- but not all -- of the positions advocated by the Moral Majority, and widespread anxiety over sexual permissiveness, homosexuality, abortion, court decisions and the moral drift of the nation, all issues the organization raises.

"I think the morals of the country are going down. Parents aren't teaching their kids enough about morality," said one affluent Dallas housewife. "Kids are getting everything too soon these days."

Among those surveyed, 67 percent disapprove of the Supreme Court ruling banning the reading of the Lord's Prayer or Bible verses in public schools; 64 percent say the sale of pornography should be banned, and 65 percent say sexual permissiveness has been bad for the country. These are all positions held by the Moral Majority.

Strong crosscurrents of moral indignation and conflicts over values run through other items in the poll. Three-fourths of those surveyed favor the death penalty for persons convicted of murder; only 20 percent oppose it. Only two Americans in 10 favor legalizing the sale of marijuana; almost twice as many favor increasing current penalties.

The Moral Majority is a minority on other issues. The Post-ABC poll found Americans supporting the ERA by 61 to 34 percent; 74 percent support legalized abortion in most circumstances. The public at large also is more tolerant on sexual questions than the Moral Majority.

Two-thirds of those surveyed say birth control devices should be made available to teen-agers; half say there is nothing wrong with sexual relations between unmarried partners (44 percent disagree).

The Moral Majority celebrated its second birthday this week by announcing an ambitious program to expand its membership from the current 4 million to 7 million during the next 12 months, and said the number of minister, rabbis and priests affiliated with it has risen to 100,000. It also revealed plans to form a new legal organization, tentatively called "Citizens Legal Defense Fund," as a conservative answer to the American Civil Liberties Union.

"Two years ago, no one believed America could be turned around, but look at the progress that has been made," Falwell said in a letter mailed to supporters. "We have the liberals, pro-abortionists, porno kinds and secular humanists upset. But if we sit back on our laurels now we'll lose the ground we've worked so hard to change. . . . Many battles must be won."

Asked about the Post-ABC poll, Cal Thomas vice president of communications for the organization, said, "We do not feel puffed up by the statistics. We only have about 25 full-time people in our national office, and Dr. Falwell has said from the beginning if we weren't expressing widely held views we wouldn't even exist."

"If we have influence, it's because government leaders are starting to listen to people they've previously ignored -- conservatives and promoralists," he added. "It's not the Moral Majority as an organization that's powerful. It is that we are expressing the fears and concerns of a large number of Americans."

Opponents of the Moral Majority agree the organization reflects genuine concerns of a great many Americans. "They do have a base. People are concerned with morality in a general sense," says George Cunningham, executive director of Americans for Common Sense, a group set up by former senator George McGovern to counter the Moral Majority and other New Right groups.

Cunningham, however, claims the Moral Majority twists popular support for issues into undesirable ends. He says, for example, that almost everyone is "against smut peddlers," but there is little support for taking dozens of popular books that various Moral Majority groups consider pornographic out of libraries.

A total of 1,533 persons was interviewed by telephone in the Post-ABC poll from May 18 to May 20.

Asked to rate how much influence seven groups have over American life, those who said they knew of the Moral Majority tended to rank it significantly behind the news media, big corporations, and labor unions; ahead of Jews; about on par with Catholic church, and only slightly behind military leaders.

The public at large says all these groups, except military leaders, should have somewhat less influence than they now have. It is particularly interested in seeing the influence of labor unions, big corporations and the new media reduced dramatically.

A total of 1,533 people were interviewed by telephone May 18-20 in the Washington Post-ABC News poll on attitudes of Americans toward the Moral Majority and other issues. Theoretically, figures based on that many interviews are subject to a sampling error of about 2.5 percent in either direction 95 percent of the time.

Figures based on subgroups are subject to a slightly higher theoretical margin of error. For example, about half those interviewed said they had heard or read of the Moral Majority. Figures based on that part of the sample are subject to a theoretical margin of error of about 3.5 percent in either direction.

The latest available U.S. census figures on age, sex, education and race were used to adjust the sample slightly so that it matched the overall population in those characteristics.