Boston — These are trying times for Boston.
One of the city's most persistent problems - racial animosity - has resurfaced just as the nation's oldest continuing civil-rights organization, the National Association for the Advancement of Colored People (NAACP), is about to hold its annual convention here. Community organizations are working to ensure that the more than 5,000 civil-rights activists scheduled to arrive by June 27 don't find a city divided against itself - along racial lines.
But it could prove to be an uphill battle. The area has witnessed a series of racial incidents recently. Although arrests have been made in the latest one, the underlying tensions remain high.
On June 2, three black families reluctantly announced they would abandon subsidized leased housing on a so-called ''white block'' in the Dorchester community of Boston.
Declaring that they could no longer risk their lives amid repeated rock and bottle throwing incidents, firebomb attacks, ''nigger'' graffiti, and vocal abuse, the families of Bernet Singletary, Mamie Jowers, and Egypt Walker asked the Boston Housing Authority (BHA) to move them to a public housing project for their own safety. They had lived in the subsidized triple-decker apartment building since Dec. 13.
Upset by this turn of events in a program designed to offer low-income people an alternative to traditional housing projects, Lewis H. Spence, receiver-administrator of the BHA, has demanded that Mayor Kevin H. White take action to curb racial confrontations in the city.
''I know of no other housing authority that must include among its regular duties the relocation and rehousing of victims of racial violence,'' he says. ''When will the city's leadership make clear that such violence is repudiated by Boston and its citizens? Most of all, where was the mayor?''
Criticizing what he calls ''segregation by violence,'' Mr. Spence proposes that Mayor White take these steps to prevent future incidents:
* Establish a special force of racially mixed teams of police specifically trained to handle volatile situations.
* Expand the police Community Disorders Unit to include an investigative arm, ''at least during the summer.''
* Coordinate procedures of the Boston Police Department with local, state, and federal prosecuting attorneys to initiate ''swift and competent prosecution'' of law violators.
* Use City Hall and Boston Committee staff members to defuse racial violence.
* Offer ''personal leadership to galvanize and support that great majority of Boston's citizens who repudiate racial violence.'' When the mayor does not speak out, ''others pull back,'' Mr. Spence says.
Mayor White and the city's police commissioner charge that the BHA moved the families into the white neighborhood prematurely.
Attempts to curb the Dorchester racial attacks met with little success. White and black residents of the community held several rallies and meetings, provided neighborhood watches, and called the police after each incident, but could not agree on unified action. Police surveillance did not halt antiblack activities.
But an intensive, month-long investigation by Boston police did result in the arrest of four white males in connection with the May 19 firebombing. The investigation was aided by information provided by white families.
Now, the Boston Committee, formed in 1980 by Mayor White and local corporations to promote racial harmony, has initiated further efforts to bring black and white community and business leaders together to develop a means of creating harmony in Dorchester, an area beset by racial distrust.
''We have found that tensions are high in this area, and sporadic flare-ups throughout the city make it difficult to pursue long-range goals,'' says Frank N. Jones, president of the Boston Committee. ''We are working to bring more harmony to a community that has had its share of incidents.''
Suburban Boston, meanwhile, is alarmed by the spread of antiblack and anti-Jewish activity among the young, especially increased Ku Klux Klan demonstrations and the white eighth-graders' Hate Jews and Niggers Organization of America in the quiet town of Manchester, north of Boston. The school reportedly enrolls only six Jewish and two black students in a student body of 500.
The Massachusetts Commission Against Discrimination (MCAD) condemned this development and what it calls ''outbreaks of racial and anti-Semetic incidents'' in other suburban communities such as Weymouth, Milton, and Needham.
Chairman Leon A. Brathwaite II says the MCAD has formed a task force of concerned organizations to develop a program ''to change perceptions and stereotypes in our youth which result in harassment and violence toward others.'' He hopes by fall to complete an educational package and make it available to schools, organizations, and institutions.
The New England Conference of the NAACP has protested the approval of Ku Klux Klan rallies in various New England communities and has established a ''Klan Watch.''