Fannie Buxton, a 28-year-old Montgomery County homemaker, quit the Democratic Party eight weeks ago at a voter registration table the local Young Republicans club set up at the Giant Food store in her Germantown neighborhood.

The same Saturday, at the same booth, Daniel R. Duggan, 27, also switched his party affiliation to Republican. Like Buxton, Duggan was a child of Democrats who became one himself when he turned 18. But in 1980, he and Buxton crossed party lines and voted for President Reagan; both plan to vote for him again this November.

Changing his political affiliation at the local supermarket "was a very convenient thing for me," said Duggan, a Federal Express sales representative. "I had given it a lot of thought beforehand . . . and it seemed like the perfect opportunity." Buxton said she registered as a Republican largely because of Reagan's record and because "my husband I are doing better financially ".

Duggan and Buxton are part of a tide, strong even by election-year standards, that is sweeping Montgomery County and other Democratic bastions around Maryland. Hundreds of voters, many of them lifelong Democrats like Buxton and Duggan, and others who never registered, have stood in line at registration booths across the state to sign up as Republicans.

Naturally enough, Reagan campaign strategists are exulting over the news, particularly after spending $8 million earlier this year in 28 pivotal states to line up a reported 2.2 million new supporters of the president.

Maryland Democrats, while discounting the three-month surge in new Republican registrants as little more than an election-season blip, are nonetheless worried about the trend. Some believe the last-minute increase could presage a Reagan victory in such counties as Montgomery, Howard and Anne Arundel.

"When there's an upturn in Republican registration, the county's gonna go Republican," said Jay S. Bernstein, chairman of the Montgomery Democratic Central Committee. Montgomery County, where Democrats outnumber Republicans nearly 2 to 1, "is not as liberal or Democratic as some people believe it is," Bernstein added.

Indeed, last month, for the first time in more than a decade, new Republican voters outnumbered new Democrats in Montgomery, 2,638 to 2,564, according to elections officials. Between June and August, the county GOP increased its share of new voters from 33.4 to 40.8 percent.

And new Republicans outnumbered or tied the Democrats this summer in Anne Arundel, Howard and St. Mary's counties, in numbers that far outweigh their actual proportion of the electorate, according to elections administrators in those jurisdictions.

No one is more surprised by the success of the Republican drive for new voters in Maryland than Republicans themselves, several party officials said earlier this week. Their success is loaded with irony, for it has come in a state that probably will be won by Democratic presidential candidate Walter F. Mondale. And it is due largely to voter registration techniques perfected decades ago by the Democratic Party.

"We Democrats used to say, 'The Republicans may have the money, but we have the people,' " said one local official active in the Mondale campaign. "Now it seems the Republicans have the people, too."

"It's because we're going back to the basics," said Ellen Conaway, 27, a Reagan campaign staff member who is one of four national coordinators of GOP voter registration. Conaway, who advised Montgomery County Republicans on voter drives like the one at the Germantown Giant, said the party four years ago "had gotten very computerized and high-tech. Now we're going back to the shoe-leather stuff."

If the "shoe-leather stuff" is the least glamorous part of a presidential election campaign, it often is the most rewarding, as Brian J. Berry discovered this summer. Berry, 26, cochairman of Reagan's Montgomery County effort and president of the county's Young Republicans, has been scouring the county for new Republicans since late June.

He has found them by the dozens.

June 23 was a classic example: 400 Republican volunteers knocked on doors in three specially targeted precincts in Gaithersburg, a booming area that is home to an increasing number of young professional couples. At the same time, party regulars set up a registration booth at Montgomery Mall in Bethesda, hoping to catch shoppers as they walked to and from the fashionable stores.

By day's end, the Republican party had won about 400 new members in Gaithersburg and 114 converts at the mall. Sixty-seven people at the mall registered as Democrats, 72 as other or no affiliation.

"What we did is precisely what Democrats have been doing for years and years," said Berry, who works at a Rockville advertising firm. "We've gotten the religion, that's all."

Targeting specific segments of the voting population has worked for other Montgomery Republicans. The local Hispanic Republican Club, for instance, says it is halfway towards meeting its summer goal of signing up 1,000 Republican voters.

Montgomery "Hispanics are coming out in droves because of Reagan," said club president Armando M. Lago, who runs his own transportation consulting firm in Bethesda.

In April, believing their fellow Republicans were "sort of scared of registration," Lago and others launched a modest voter drive of their own, targeting middle-class and affluent Hispanics in the Bethesda-Rockville corridor. One Sunday afternoon, for example, they registered dozens of people who attended a Spanish mass at Our Lady of Lourdes Catholic Church in downtown Bethesda.

Another day, the club made a foray into the poorer sections of nearby Silver Spring, but abandoned it after a couple of hours when many more people registered Democratic than Republican. And yesterday afternoon, about 200 people, most of them professional men, paid $20 each to attend a party at Lago's Potomac home to meet a key Reagan adviser on Hispanic affairs, Robert Estrada.

Lago, 44, believes he holds the key to successful voter registration drives: "It's all targeting," he said. "There are areas where the proportions are against us. But we now know we can go into other parts of this county and for every Democrat, we get five Republicans."