By LITA LELYVELD; Nita Lelyveld is a staff writer for The Tuscaloosa (Ala.) News.

Until recently, the people of this small town in the southwest corner of Mississippi didn't see much in common between themselves and Shakespeare. They read his plays in school and left it at that. But when the Cornerstone Theater Company showed up and started building a stage in their local movie house, Shakespeare became the talk of the town.

The 11-member traveling troupe arrived in Port Gibson last November, moved into an old, abandoned boardinghouse on the main street and immediately began auditioning people for an adaptation of ''Romeo and Juliet,'' to open in February. They made announcements in the local churches and schools and handed out leaflets to everyone they saw. One company actor, Ashby Semple, even stood in the street outside the theater, stopping traffic with the words, ''Want to be in a play?''

When the cast list went up several weeks later, Edret Brinston, an 18-year-old black high-school senior, had been chosen as Romeo, with Amy Brenneman, a white Cornerstone actress, as his Juliet. More than 50 other local residents had been selected to serve as the play's cast, crew and musicians.

The ''Romeo and Juliet'' Cornerstone had in mind was not the traditional love story set in a time and place very foreign to small-town Southerners. Instead, they chose to anchor the play in Verona, Miss., a fictional locality meant to bear a striking resemblance to modern-day Port Gibson.

There is more than one Port Gibson, as company members were soon to realize. There is the fairy-tale Port Gibson of Church Street, with its extraordinary collection of balconied antebellum houses, painted white and pristinely preserved, which, the townspeople say, Gen. Ulysses S. Grant spared during the Civil War because they were ''too beautiful to burn.'' The majority of the town, however, whose population of 2,200 is largely black and poor, lives in the other Port Gibson, which starts just behind this showcase street, many in dilapidated cabins along unpaved roads.

While Claiborne County, in which Port Gibson is situated, is 80 percent black and is governed largely by black officials, the town of Port Gibson has a white mayor and a virtually all-white private academy. The public schools, on the other hand, are predominantly black. There is little overt racial tension in the community, but there is equally little opportunity for social or institutional interaction between races.

Cornerstone first heard of Port Gibson through Mississippi: Cultural Crossroads, a community organization dedicated to bringing the arts to Claiborne County. The organization, which is supported by local, county and state grants, as well as through its own fund-raising, found Cornerstone living and rehearsal space and helped with money for production expenses.

While the company was not sure at first how far it would take the parallels to the social structure in Port Gibson, it ended up casting the play almost entirely along racial lines. All the Montagues, including Romeo, were black, and all the Capulets, including Juliet, were white, and Juliet's nurse was played by a black woman.

''We're not forcing this concept on the play,'' said the director, Bill Rauch, shortly after the cast list went up. ''The play is about a society that has a division in it, and racial lines do form some divisions in this community. But reinforcing that idea with racially divided casting was very scary, because, of course, we don't want to propagate racism by presenting it. As in Shakespeare, the theme of our production is going to be unity rather than division.''

Adapting classic plays to mirror contemporary realities is central to Cornerstone's purpose. Founded in 1986 by Mr. Rauch and the managing director, Alison Carey, who graduated in 1984 and 1982, respectively, from Harvard, the company aims to make theater an integral and relevant part of ordinary American life. Most of the communities they choose to visit have had little exposure to live theater.

Since that first summer, when it staged Thornton Wilder's ''Our Town'' in Newport News, Va., the company has traveled all over the United States, living mostly in small communities for two to four months and recruiting residents to serve as cast and crew in their projects. The towns contribute housing and performance space. In addition to their main production, the company members teach and perform in the local schools.

The Port Gibson project was Cornerstone's 10th residency. The company is currently conducting its annual fund-raising tour, and will hold a reception in New York to describe their work at 6:30 P.M. tomorrow at the Tower Gallery, 45 West 18th Street. Future plans include residencies in Montgomery, W. Va., and Eastport, Me., next year and a visit to the Soviet Union in January 1991. They also plan to create a touring alumni show with cast members from all their previous residencies in the summer of 1991.

Mr. Rauch and Ms. Carey, as undergraduates at Harvard, had often discussed forming a traveling theater group. ''We thought we'd bring a show to a community and ask them what they thought of it through forums and discussions. But that's not the way you establish a real dialogue with someone,'' Ms. Carey explained. ''We decided that, if we were sincere in our desire to learn from people what makes good theater and whether theater is important, then we had to be in the trenches together.''

The real turning point for Cornerstone came with its second production, when it arrived in Marmath, N.D., a town of 193 people, planning to stage ''Hamlet.'' The town had expected something more along the lines of a dinner theater and expressed little interest in the project.

''It all began to change when we got to North Dakota and saw the locals dealing with Shakespeare,'' Mr. Rauch said. ''There were so many words that were so irrelevant to their vocabulary. We began to ask ourselves, what if we used some words that had more of the impact on the audience that Shakespeare intended them to have? That way you sacrifice some of the poetry, but you gain a lot in terms of the drama.''

That first adaptation, ''The Marmath Hamlet,'' was set in the Wild West. Hamlet began his ''To be or not to be'' soliloquy in the shower, drinking a beer, and in one of the unplanned incidents that have since become a part of Cornerstone lore, the town grocer, Gus Watson, said ''Hi'' instead of ''How now, Lord Hamlet?'' when he forgot his lines during one of the performances.

Other projects have included ''The House on Walker River,'' an adaptation of Aeschylus' ''Oresteia'' performed on the Walker River Indian Reservation in Shurz, Nev.; an adaptation of Moliere's ''Tartuffe'' in Norcatur, Kan., and ''That Marfa Fever,'' Cornerstone's version of Noel Coward's ''Hay Fever,'' performed in Marfa, Tex. In the summer of 1987, the company went to Miami Beach and transformed ''The Dog Beneath the Skin,'' by Christopher Isherwood and W. H. Auden, into a forum for the expression of the community's feelings about the AIDS crisis.

Cornerstone receives financial support for its projects, which cost an average of $50,000 each, from a variety of sources. While the bulk of its income this year has come from individual contributions, it has also solicited grants from private foundations and state arts and humanities councils, receiving important support from the Virginia Commission for the Arts. To keep its work widely accessible, the company charges little or no admission for its performances. It also donates part of all box-office earnings to the towns, to encourage them to continue with theater on their own.

''Romeo and Juliet,'' with a cast of 47, was Cornerstone's largest show to date. ''The more people there are from the town in the play,'' said Ms. Carey, ''the more the play is going to reflect the town.''

The company experiments with a variety of media to make its work as lively as possible. Music, for instance, is a part of each production, with the Cornerstone composer David Reiffel writing both scores and lyrics. ''Romeo and Juliet'' contains 14 songs ranging in style from gospel to pop, almost all of whose words are taken directly from the play. Shakespeare's original language is often easier to preserve as lyrics, rather than dialogue, Cornerstone finds.

Members of the company do not feel that, working with nonprofessional colleagues, they lower their standards. If anything, they say, they are the ones who gain most from the experience.

''We're proud of the good that we do in communities, but frankly we're not doing it in order to do good. We're doing it because this is how we can best grow and do better art,'' said Mr. Rauch, who worked as Peter Sellars' assistant director at the Kennedy Center in Washington before founding Cornerstone.

A tremendous amount of time and energy goes into each community project. The cast of ''Romeo and Juliet,'' for example, rehearsed on an almost daily basis from November until February. The set for the production, too, was elaborate, especially considering that a stage had to be created from nothing. Meant to evoke the mood of an antebellum home, it featured large columns and a typical Southern screened porch that served as Juliet's balcony.

Many weeks were spent, too, on the adaptation of the play, and changes continued throughout rehearsals. Cornerstone members take their time with their productionss, waiting until they have felt out the concerns and rhythms of the community before trying to incorporate them into the text. They also test out controversial ideas on the cast to make sure they are on the right track.

The resulting script for ''Romeo and Juliet'' was both very much in the spirit of the original play and a critique of Southern society and racism. Lord Capulet, for example, became Mamaw, Juliet's grandmother and a harsh and unbending Southern matriarch. Tybalt, played by a company actor, Ashby Semple, was a racist young woman full of hatred for blacks. Friar Lawrence, played by a company actor, Peter Howard, became Father Lawrence, a Catholic priest forced by Romeo to put into action the liberal beliefs he espouses.

While the cast seemed to have little problem with the basic interpretation of the play, some did raise questions when they first saw Romeo and Juliet kiss passionately on stage. They asked Mr. Rauch to tone it down, not because they objected, exactly, but because ''the town'' would be upset.

Mr. Rauch stood his ground, however, explaining that the intimate relationship between Romeo and Juliet was central to the play, and the production survived the storm. No one left the cast, and the subject was dropped.

For Mary Curry, an outspoken black cast member, the Cornerstone portrayal of a mixed couple is unequivocally positive.

''I think it's great,'' she said. ''I think it's time. Dr. King died for this, and I don't see anything wrong with it. I was a little girl when he died, but I believe in his dream - let's walk hand in hand and be equal - so I have no problem with it.''

The parallels made in the production between life in Verona and life in Port Gibson were unmistakable. Juliet, Tybalt and their friends wore the uniforms of the local Chamberlain-Hunt Academy, for example, while Romeo's crowd went to Montague Memorial High, clearly a stand-in for the town's public school. Ms. Curry, just elected to her first public office as election commissioner of her district, played the Mayor, Cornerstone's version of Escalus, Prince of Verona.

Similarly, after evening rehearsals, Mr. Brinston, who plays Romeo, and Earl Wilson, who plays Benvolio, would dance and lip-sync to rap music. This was incorporated into the script, with Romeo rapping the descriptions of his feelings to Benvolio.

Long before the scheduled start of the opening night performance, a line had formed outside the Trace Theater. Ms. Carey and the company manager, Paul Bostwick, couldn't help grinning as they put up notices to announce that tickets for that evening were sold out. Not only had they already taken enough reservations to fill the house for most of the three-week run, but the audience they had attracted was diverse, with people of all ages, black and white.

Ms. Carey found the audience's reaction deeply moving and gratifying. ''I noticed that two women, an older black woman and an older white woman, were sobbing during the final scene,'' she said. ''It was very lovely to see and very healthy, I think. This was a very successful project.''

In a forum held after the production was over, company members were surprised and pleased by the frankness of the discussion, which focused on such touchy subjects as the de facto segregation in area schools.

''They were very forthcoming,'' Ms. Carey said. ''But there were some sad parts, too, like when we talked about the friendships that had formed and how unusual it was to see black kids and white kids playing together. I remember one of the black women saying that she wondered if her son's friendship with a white girl his age in the show would continue.''

A month after Cornerstone departed, the visit has not been forgotten. ''Whenever I go into the shops here, people ask me about Cornerstone and say they're sad they've gone,'' said Patty Crosby, director of Mississippi: Cultural Crossroads. ''They say things like, 'We miss those young people.'' So clearly a void is being felt, and it will be interesting to see how the community will fill it. I'm optimistic that they will somehow.''