Politicial support for Rep. Robert E. Bauman (R-Md.) began to erode yesterday, as three conservative organizations and the largest newspaper in his congressional district called for his resignation.

Bauman, charged last week with soliciting sex from a teen-aged boy, remained in seclusion yesterday at his home near Easton, on Maryland's Eastern Shore.

Paul Weyrich, head of the Committee for the Survival of a Free Congress, urged Bauman to resign both his First Congressional District seat and the chairmanship of the American Conservative Union, saying the allegations of homosexuality and alcoholism have left Bauman "no longer a credible spokesman" for conservative causes.

Flanked by representatives of Religious Roundtable and the American Association of Christian Schools, Weyrich told a press conference that "as much as we have compassion and sympathy for his plight, we are also carrying on important moral and philosophical matters, and these battles will be hindered if Bob Bauman remains in any position of leadership."

The three organizations are among more than a dozen politically conservative groups that are part of a loose coalition known as the New Right. Along with the ACU, which is headed by Bauman, they espouse issues such as anti-abortion amendments and opposition to the Equal Rights Amendment. Bauman has been a leading spokesman for their positions in Congress.

The Salisbury Daily Times, in an editorial yesterday, said "it is time for Bauman to reevaluate his position in the campaign, and in light of the most recent revelations, he should resign from Congress and withdraw from the race. It is the only honorable thing to do," said the newspaper, which endorsed Bauman in 1976 but not in 1978.

Perhaps even more damaging to Bauman's long-range political future was the comment by Rep. Marjorie S. Holt (R-Md.), who said Bauman should go ahead and seek reelection so that his seat would not be captured by a Democrat, but that he then should consider resigning, once conservatives have time to find a politically acceptable successor.

Holt, one of Bauman's closest political allies in the House, represents the adjoining Fourth District of Maryland. She said for Bauman to quit now "would seem to be unfair" to residents of the district.

She admitted that there is "a lot of resentment" about Bauman's failure to tip off his political friends that "this thing was coming." She said she learned about the charges last Thursday night, only after hearing rumors about it at the Capitol. "I called Bob, and he just read me the same statement that he put out to the press next day," Holt said.

Holt said that she is still "unable to sort this out," because the news came as "such a shock, a surprise."

Willard Morris of the Maryland Board of Elections said yesterday that it is too late for Bauman to have his name removed from the Nov. 4 ballot. Morris said state law permits a candidate to decline nomination "up to 70 days before the election, and that time has long since passed."

If Bauman should resign anyway, Morris said, his name nonetheless would appear on the ballot, along with Dyson's.

Unlike vacancies in the Senate, which are filled by appointment by the governor in most states, House vacancies can be filled only by elections.

Republican National Chairman Bill Brock said yesterday the GOP is ready to provide money for Bauman's campaign. Bauman has not sought help from the national party because he was considered an overwhelming favorite for reelection.

"I'd like to support his congressional race in any way I can," said Brock.

"He's a very able person."

Weyrich, 37, said the decision to call for Bauman's resignation was "the most difficult task" of his 20 years of conservative activism. But it was necessary, he said, not because Bauman had sinned, "for which he is forgiven, because we all are sinners," but because "of his leadership position" in the conservative movement nationally.

"Since Rep. Bauman, unlike the ordinary elected official, is widely known across this country, his responsibility to the cause is much greater," Weyrich said. "We recognize the agony that this problem has caused him and his family and we hope and pray that he will, in fact, repent and redeem himself. However, the cause which he has helped to represent is greater than any one individual.

"As much as we have compassion and sympathy for his plight . . . it is impossible to defend his alleged actions. The conservative and pro-family movement ordinarily concerns itself with the public conduct, rather than the private lives of elected representatives . . . In this case, however, Congressman Bauman's personal conduct has been called to the nation's attention, and therefore we cannot remain silent," Weyrich said.

Both Weyrich and Bill Marshner of the Religious Roundtable said they could not accept alcoholism as an excuse for Bauman's behavior.

Marshner, whose organization sponsored the religious rally in Dallas last month at which Republican presidential nominee Ronald Reagan spoke, said he could find "no plausible relationship" between Bauman's sexual activites and his statement that he is an alcoholic.

Bauman entered a plea of not guilty, and agreed to enroll in an alcoholic rehabilitation program, after the Justice Department charged that he solicited and then engaged in oral sodomy with a 16-year-old boy early this year near Capitol Hill. Sources said the federal investigation was prompted by an informant's claim that the congressman was involved in homosexual solitictations of minors.

Marshner said that "there is a distinction between personal repentence and public amends. When a guy says, 'I repent, I repent,' and then plea bargains, that has all the earmarks of a coverup."