The old men hunched over their coffee cups this morning at the town diner, their uneasy silence haunting a place that normally buzzes with talk and laughter. A few yards away, the bold headlines of the Easton Star-Democrat stacked on the counter did the talking for them: "Bauman Faces D.C. Sex Charge; Admits He's An Alcoholic."

Along the narrow streets of this Eastern Shore town, the home of Congressman Robert E. Bauman, and throughout the state where he has been a respected public figure for many years, men and women reacted to today's news as if a tragic secret had burst out.

"It kind of makes you wonder: 'Who else?'" said a 50-year-old businessman who is part of the regular morning coffee crowd here at Trader's Drugs. "My wife saw it on TV last night. We just looked at each other in disbelief. He's the last one we'd expect this of."

Many residents of Bauman's rural and applie-pie conservative congressional district said they would have preferred not to know about the sex charge lodged against him across the bay and a world away in downtown Washington this morning. Some said they simply could not believe any of it was true. But the career of the three-term Republican representative, according to fellow politicians here and elsewhere, now depends on how the folks back home respond to the Justice Department's allegation that Bauman had sodomized a teen-aged boy.

Bauman's Democratic opponent this fall, state Del. Roy Dyson of St. Mary's County, said that he reacted to the news much like many of the voters in his sprawling district. He was called away from a dinner table out on the campaign trail, he said, to get the stunning report over the telephone. "I was so surprised, I guess I just didn't believe it. I walked back and sat down and didn't say anything. I just kept thinking about it."

Dyson, who lost to Bauman by four percentage points in 1976 but had not been considered a strong threat to the conservative incumbent this year, said he then called his family and told them: "We don't get involved in any campaign on an issue like this."

Today, Dyson was so besieged by phone calls on the Bauman incident that he had to skip most of his scheduled appearances. To every caller, he had the same message: He "absolutely would never get involved in a campaign reflecting negatively on Bauman or his family in a personal way."

"I'm sympathetic to his plight," said Dyson. "It will be a personal tradegy to his family. We have fundamental differences, but I'm not an insensitive person."

Bauman's colleagues in Congress and in Maryland politics from Sen. Charles McC. Mathias to Gov. Harry Hughes and local central committee members, expressed sympathy for the representative and his family today, but many of them were so shocked or confused that they could add little else. "There's so much that could be to this story that I don't know," said Irving Ober, chairman of the Republican Central Committee in the Eastern Shore's Caroline County. "I don't think it's anything right now but weird."

Perhaps tactfully, both elected officials and citizens tended to confine their remarks today to Bauman's own story of a battle with drinking, despite the assertion of his local doctor and friend that he was not an alcoholic. All those who had known the former state senator and Capitol Hill staffer agreed, too, that they had never known Bauman to drink heavily.

"He was as strait-laced as they come," said Repulbican State Sen. Ed Mason of Cumberland, who was Bauman's seatmate in Annapolis.

John Hargreaves, a veteran Demoractic state legislator from Caroline County, expressed the feelings of many political leaders when he said that if the voters sympathized with Bauman's revelations about his struggle with alcoholism, and his statement that he had returned to "a state of grace," the damage to his popularity could be minimal.

"Many people have learned to live with the problem of alcoholism," said Hargreaves. "People might understand that. But the sodomy is difficult to assess. There are a lot of deeply religious people on the Eastern Shore, very homey, very traditional people. . . . It might be a problem.

Indeed, Bauman gained much of his recognition in Congress and popularity at home by articulately championing the traditional values of family and home. He upheld this standard both in his votes and his sharp rhetorical attacks on those who he believes were less virtuous.

The Moral Majority religious lobbying group headed by the Rev. Jerry Falwell has always given Bauman high ratings for his voting record. Only last summer, Bauman was one of 290 House members who voted for an amendment prohibiting a government-funded legal service from "promoting, defending or protecting homeosexuality." He also cosponsored a "Family Protection Act" to "promote the values of family life through education, tax credits and other matters."

Bauman, who quickly emerged as one of the most quotable conservatives in Congress after his electon to the House in 1973, once noted during a debate that Wayne Hays, who had accused him of knowing little about foreign affairs, "had problems with affairs himself." Another time, when asked about his future political ambitions, Bauman replied: "Like Kennedy says, I'll cross that bridge when I get to it."

Now, Bauman will have to confront some of the same harsh judgments he once rendered on others. Bill Closson, a chicken farmer who has been driving to Easton on Fridays to do volunteer work for the Repulbican Party, said this morning that he would not abandon the congressman because "you can't use alcoholism as an excuse for anything you do."

Another supporter, Vernon Sultenfuss, a Queen Anne's County commissioner who sponsored a bull roast for Bauman in August that raised $37,000 for his campaign, said the congressman would have to "let us volunteers know what the situation is firsthand. I'm very disappointed. If this is true, it will take a tremendous effort by our campaign to overcome, and well, I just hope it's not true."

Those who still count themselves among Bauman's supporters blamed his troubles on the pressures of politics and the frailties of human nature. Some Eastern Shoremen questioned the timing of the charges and the purity of the Justice Department's motives.

Said state Sen. Frederick C. Malkus, the silver-haired dean of the State House who lost to Bauman in the 1973 congressional race: "When you get caught shooting ducks late it's because someone turned you in to the game warden. Something had to have started this, but I don't think we'll ever know the whole story."

Even among the faithful in the historic town, however, there was painful discomfort this morning. 'I thought he was a boy scout. I thought of him as having a halo around his head," said a crestfallen elderly woman from the local women's Republican club. And at Bauman's district office, staff members sat under a pall of silence and refused to answer questions from reporters.

Three miles away, in his white, wooden, two-story house set far back from a country road, Bauman spent the evening alone with his wife and four children. His car, with congressional license plates, was parked outside, next to a van that was decorated with billboards saying, "Bauman . . . He works for You."

Dressed in sports shirt and tan pants, Bauman answered the door tonight when a reporter came seeking an interview. His face drawn, he kept his eyes lowered and politely declined to answer any questions. "Under the circumstances, I think you can understand that we'd rather not talk to anyone," he said softly.