Hundreds of students - black and white and shouting newly minted protest chants against racism - rallied and posted picket lines yesterday as the United States and South African tennis teams prepared for their Davis Cup matches at Vanderbilt University.

Scores of relaxed police looked on as South Africa's official suppression of blacks was denounced in songs and in sayings and on signs by protesters. They were gathered outside Memorial Gymnasium to make the match's patrons "make a decision" on whether to cross the picket lines and watch a South African team play.

As spectators began arriving for the 6 p.m. match play, some 200 picketing demonstrators booed and hissed loudly at them and shouted, "Join the march, not the match." Protestors called them racists and told them they ought to feel guilty.

"Damned idiots!" said J. T. Taylor after walking through a picket line with his wife Helen. "I don't think the South African team represents the South African government any more than the U.S. team represents the Carter administration."

He described himself and his wife as tennis buffs and said. "We've never been able to see a Davis Cup match before, and we're anxious to see one."

The city and university were divided over being host to the Davis Cup Matches.

Benjamin Hooks, executive director of the NAACP, who initially had called for the most massive civil right demonstration since the 1960s, said yesterday he now only hopes for as many as 2,000 participants.

Some 360 uniformed police have been assigned to the march route. Days off have been canceled and police will work 12-hour shifts to ensure that expectations of a peaceful affair are met.

Silent participation in the protest or fear of possible difficulties apparently have cut ticket sales below the break-even point of 4,000 a day.

About 3,000 tickets were sold for last night's two singles matches. Joe C. Davis, a Nashville businessman and Vanderbilt trustee and alumnus, has agreed to absorb any losses up to $88,000. Davis provided the backing after an earlier sponsor withdrew because of the controversy over South Africa's participation.

A spokesman for the U.S. Tennis Association said his group has an excess of offers to host future Davis Cup competitions despite the Nashville protest. He said he doubted those offers would be altered by a dollar loss here because of South Africa's participation.

Whatever the impact on ticket sales, the protest and today's scheduled march have drawn international attention to a city better known for its Opry.

Students from Vanderbilt and other universities converged on Memorial Gymnasium at 2:30 a.m. in the cold under a lead-gray sky that sporadically dusted them with snow flurries. With the infusion of students from Fisk and other black schools, the crowd became predominantly black.

They chanted to a rhythm reminiscent of earlier civil rights and Vietnam War cries but with different words riding on that rhythm. Johannesburg, Soweto and apartheid were the key words - not Selma, My lai and peace.

The decision to host the matches has split the Vanderbilt community - both students and faculty - over whether the racial practices of South Africa are so abborrent as to, in this instance require closing the university's "open forum" concept in which all ideas are allowed free debate.

If the forum was still open, it was not free. Protest leaders solicited contributions to offset the fee the university charged for its facilities used in yesterday's rally - $500. Free speech, said a speaker through a bullhorn, is not free.