Sen. John H. Chafee may be "Mr. Republican" in Rhode Island, as his Democratic challenger cheerily concedes, but Chafee's not making a big deal over it.

The snappy green-and-white campaign brochure he was handing out at local factories the other day has pictures of shipyard workers, old folks, his wife and children, even a cow getting a friendly hug from the candidate. All that was missing was the word Republican and the face of President Reagan.

"Why rub it in?" shrugs Chafee, amiably conceding that the omission was no accident.

Indeed, partisan anonymity seems to be a simple matter of survival as Chafee tries to defend a comfortable early campaign lead against a hard-hitting assault from Democrat Julius C. Michaelson in a heavily Democratic state that gave Reagan only 37 percent of the vote in 1980.

Rhode Island political observers say Chafee is hanging onto his lead, shielded from economic and political downdrafts by voters' familiarity with his independent-minded practice of politics over the last quarter-century in Rhode Island. A "Man You Can Trust," Chafee likes to call himself.

But they do not rule out an upset if Michaelson succeeds, more than he has so far, in getting people to link a reluctant Chafee to Reagan, his economic policies and the recession that has brought high unemployment and at least one Great Depression-style soup kitchen to some Rhode Island industrial towns.

Chafee is one of a half-dozen moderate Republicans from predominately Democratic or battleground states who are counting heavily on their own records, marked by at least partial independence from Reagan, to withstand the political ravages of plant closings and double-digit unemployment.

But, even for a state where vastly outnumbered Republicans often camouflage their partisan affiliations, the distance Chafee has put between himself and Reagan is striking.

At one point, as Michaelson was accusing Chafee of voting with Reagan far more than Sen. Claiborne Pell (D-R.I.) on some selected budget issues, the Chafee camp countered by pointing out that Chafee voted against Reagan more often than all but a handful of his GOP colleagues.

Chafee does not go out of his way to criticize Reagan but is not shy about pointing out their differences on defense spending, social welfare cuts and other matters.

"The jury's still out" on Reagan as president, he said in an interview after criticizing Reagan's priorities on defense and domestic spending. Asked if he would like Reagan to come to Rhode Island before the Nov. 2 elections, he smiled and said, "In the current climate it wouldn't be helpful.

Chafee's elusiveness has made life more difficult for Michaelson, but it hasn't stopped him. With the relentlessness of the prosecutor he used to be as the state attorney general in the late 1970s, Michaelson has churned out vote after vote in which Chafee toed the Reagan line to approve cuts in popular social programs. Flatly challenging Chafee's efforts to portray himself as an independent force in the Senate, Michaelson has doggedly pursued his rival as "a foremost proponent of the Reagan economic program . . . sponsor of the supply-side trickle-down economics."

If Republicans are returned to office, he maintains, Reagan will interpret the vote as a "mandate to continue" his present course.

"Julie Michaelson is the last man that Ronald Reagan wants in the U.S. Senate," reads his campaign literature. "Send a fighter," say his billboards.

The 59-year-old Chafee has made a successful political career out of being just a little bit different: a patrician Yankee Republican in an ethnic, blue-dollar and Democratic state, a moderate in a party dominated by conservatives.

With family roots reflecting old New England wealth and influence, he campaigns with an easy, baggy-suits, down-home style that has factory workers reaching eagerly over their machines to shake his hand, a nice trick for a Republican anywhere.

In normal times, Chafee, whose political career included three two-year terms as governor and a stint as secretary of the Navy, would probably be a safe bet for a second term in the Senate. But these are not normal times.

"I think if the economy was good, Chafee would have no problem," said Len Goldman, a Providence businessman, as Chafee talked to the city's Rotary Club last week. "But it isn't good, and that gives Michaelson a chance."

Even more to the point, Republican Rep. Claudine Schneider, who shares many of Chafee's pluses and minuses this fall, put it this way: "We have the same problem every Republican has -- Reagan and unemployment."

Chafee's speech to the Rotarians illustrated the pitch he is making. Double-digit unemployment is "intolerable," he said, and jobs are the "number one priority." Military spending has "just gone too far."

But economic problems are not unique to the United States, he added, and their roots extend back "through Republican and Democratic administrations over the last 30 years."

Michaelson has accused him of voting to trim some Social Security benefits last year, but Chafee's campaign literature contends "there's no stronger fighter in Congress" for Social Security. On jobs, despite his appeals for restraint in defense spending, he proudly claims credit for submarine contracts for Electric Boat, the state's largest single employer.

With a strong record of support for the environment, women's rights and other causes that mobilize liberals, Chafee has cut into constituencies that would normally be expected to lean toward a Democrat. He was called a "hero" by spokesmen for five major environmental groups that endorsed him recently.

But organized labor has a hero in Michaelson, who served as general counsel to the Rhode Island AFL-CIO after leaving the attorney general's office and embraces many of labor's legislative goals. About 28 percent of the work force is unionized in Rhode Island, making it one of the most heavily unionized states in the country.

"Chafee got over half labor's vote before, but it will be significantly less this time," says State AFL-CIO President Ed McElroy.

As intense as Chafee is relaxed, the 60-year-old Michaelson is an engaging, articulate campaigner, a Harry Truman admirer whose scrappy style fires up the faithful. He has put the Chafee campaign on the defensive in some of his attacks on spending votes.

Perhaps more importantly, Chafee, with a campaign kitty of more than $1 million, will outspend Michaelson by about 2 to 1. Michaelson contends that his budget, not all of which has been raised, should be enough in a state the size of Rhode Island.

Ironically, if Chafee loses, it may be because of the phenomenal success that Senate Republican leaders had in rallying their troops to protect Reagan's budget cuts from proposed Democratic add-backs.

Chafee led his own losing fight to restore about $1 billion in social spending last year and helped spearhead a successful campaign this year to get the Republican leadership to forget about $40 billion in unspecified Social Security cuts through 1985. In the meantime, however, there were scores of votes in which he joined other reluctant Republicans in holding the line against the Democratic counterstrike. These votes are now bedeviling Chafee.

Two workers at a Kenney drapery manufacturing plant in Warwick, which Chafee visited recently, summed it up this way. "He's a good man, a decent man. He's come out a lot against what Reagan's trying to do," said Brendan Darcy, tool-and-die foreman.

"Chafee, he's his own man in a way, I guess," said a worker in the purchasing office who declined to give his name, "but he's still a Republican and it's uphill all the way for Republicans."