The memory of Jon Hinson, the conservative Republican who resigned his House seat after his arrest on a morals charge in Washington last February, still haunts the state party and the voters who sent him to Congress twice.

But inflation and President Reagan's budget cuts -- not the homosexual peccadillos that led the congressman to quit -- are the issues commanding center stage among eight candidates scrapping for Hinson's seat in the June 23 special election in Mississippi's 4th District.

For the Republicans, it's almost a no-win situation. If their leading candidate, a lackluster Jackson businessman who has wrapped himself in the Reagan economic dogma, doesn't win outright, they fear it will be seen as a grassroots rejection of Reagan's budget program, in a state the president narrowly won last November.

Republicans have tried hard to scratch the word "Hinson" from their political glossary.

"In your church, when the minister strays, it doesn't make the church or the Lord bad," says independent oil man W. D. (Billy) Mounger, a Republican and once staunch Hinson supporter. "When Jon Hinson strayed, it didn't make the Republican Party or Republican candidates bad."

Still, shame dies hard in this southwest Mississippi outback of mostly white, very Baptist, conservative Democrats who vote like Reagan Republicans and hold that men should be all-man, women should be ladies and homosexuality is the abomination the Bible calls it. The seat has been held by a penny-pinching Republican since 1972, when Hinson's predecessor, Thad Cochran, now a U.S. senator, first won it.

But voter apathy and disgust for politicians in general lingers months after Hinson was arrested on a felong misdemeanor charge of oral sodomy in the men's room of a House office building with a male Library of Congress employe.

"The fact that the employe Hinson was caught with was black added insult to injury here in Mississippi. There are still a zillion jokes about it," says Leslie McLemore, 40, a Jackson State University political science professor and black community leader.

The state Republican Party has moved quickly to reassure voters by pulling together at a state nominating convention behind Liles Williams, vice president of a Jackson electrical supply firm.

If no candidate wins a majority in the June 23 election, the two top vote-getters, regardless of their party affiliation under the state's primary rules, will meet ina runoff July 7, Williams, as the GOP front-runner, is expected to make it to the runoff against the ydemocratic favorite, Britt Singletary, 30, a Jackson attorney and graduate of Ole Miss.

Republicans are also touting polls that purport to show increased party identification among voters. Mounger argues that the Hinson matter "has had no effect" on the party or a GOP candidate's chances to hold the seat.

Four Democrats, three Republicans and one independent are vying for it. Among them: a state senator from Jackson, a small-town mayor, a hotel manager, a solar-energy consultant, an independent truckers' association president who was once a grand dragon in the Klu Klux Klan, and a card-carrying klansman running on a plank of white supremacy.

All the candidates generally support Reagan's economic recovery package, although some differ on tax cuts and reducing Social Security benefits.

Williams has portrayed himself as a textbook disciple of Reaganomics, preaching federal parsimony and tax cuts.

While he has low name identification, Williams enjoys such advantages as a $200,000 campaign war chest, slick TV ads and a well-oiled state party machine and aan ability to canvass, poll and staff phone banks that is openly envied by Democrats.

Democrats Singletary, a former aide to Sen. James O. Eastland, has more name recognition than money, having finished an embarrassing third behind McLemore last November in an unsuccessful attempt to unseat Hinson. Singletary has delicately sidestepped any verbal jabs at Ronald Reagan by name, because of the president's popularity here. Rather, he takes aim at some of the more "painful" budget cuts targeted by "the administration."

"There's nothing to be gained by attacking Ronald Reagan," he said.

Hinson's reelection last fall surprised many Bible Belt observers because the congressman had disclosed a 1976 arrest on a morals charge and a narrow escape from a fire that struck the Cinema Follies, a Washington theater frequented by homosexuals.

"You'd think a man who had acknowledged frequenting a homosexual theater would have been run out of Mississippi," Mounger said at the time. "But some folks would rather have a queer conservative than a macho liberal, and they may be right."