When Rep. Claudine Schneider challenged former Democratic Rep. Edward P. Beard in her first bid for Congress four years ago, Beard chided her at one point for campaigning too hard.

"Quit working so hard," she recalls him telling her. "In a few weeks you'll be back home scrubbing floors and washing dishes."

Schneider, a moderate Republican, did lose, but two years later she washed up and polished off Beard to become the first woman elected to major political office in Rhode Island.

Now, after helping lead the "Gypsy Moth" revolt by GOP moderates against many of President Reagan's budget cuts over the past two years, Schneider is favored for reelection despite a recession riptide that threatens Republicans in heavily Democratic Rhode Island.

Moreover, according to Suzanne Perry, head of the Rhode Island Women's Political Caucus, Schneider's odds-defying challenge four years ago has resulted in a surge of women into the entry ranks of state politics and encouraged more women to aim high for elective office.

"It opened the way for others to follow . . . and they did," said Perry.

Rhode Island's secretary of state, one of five statewide offices to be filled in the Nov. 2 elections, will be a woman no matter who wins. Republican Susan Farmer narrowly lost in a bid for secretary of state in 1980 but came back to run again this year, and the Democrats put up a strong woman candidate, Victoria Lederberg, against her.

The Republicans also have fielded a nun, Sister Arlene Violet, to challenge State Attorney General Dennis J. Roberts.

Rhode Island, with its ethnic tradition of male-dominated government, has not been converted overnight to unisex politics, however.

Schneider earned a reputation in Washington as an up-and-coming lawmaker. She took a leading role on issues ranging from defense to education in the 1981 and 1982 budget fights, and brought back some trophies for the home folks, including shipbuilding jobs and at least two urban development grants. But she's staying ahead in Rhode Island only by running harder than anyone else.

Women activists also claim it took some heavy pressure to get the Democrats to accept Lederberg.

But the measure of how far Rhode Island has come in four years may be seen in Schneider's congressional race where her Democratic opponent, James V. Aukerman, a popular state legislator, claims there is no dispute over "women's issues" like abortion and sex discrimination because he agrees fully with Schneider on them.

He also touts the fact that most of his campaign headquarters staff are women.

"The difference is not over women's issues, it's a matter of being a Democrat or a Republican," he says.

Maybe. But random chats with voters earlier this month indicate that old habits die slowly.

"Yeh, it bothers me. I didn't think much of the WACs or WAVEs either," said John Fusaro Sr., as he watched Schneider walk by in Westerly's Columbus Day parade. "But she's an educated woman, and I like that," he added approvingly.

"I guess a woman has to prove herself more than a man," said Lowy Cagle, as he cheered for Schneider at a Warwick rally. "But she's proven herself."

Perry adds that women seem to have to run and lose once before winning in Rhode Island.

But in the process they bring women into politics in successive waves, as Schneider's campaign illustrates.

She has 400 to 500 volunteers, about three-fourths of them women recruited from her three campaigns. Most never were involved in politics before her campaigns.

Two who staff her Warwick headquarters help tell the story.

Campaign manager Liz Harris, 23, dropped out of Brown University in 1980 to raise political action committee money for Schneider, then worked in her Washington office and came back last fall to help put the reelection campaign together.

Paula Buckley was a local resident, never involved in politics except to help a friend in a local campaign, who met Schneider at a local arts festival in 1978.