More than 500 angry, sign-waving parents and schoolchildren rallied at the District Building last night to protest Mayor Marion Barry's proposed cuts in next year's city school budget.

The artfully choreographed demonstration -- organized by Parents United for Full Public School Funding -- began on the steps of the building with cheers, chants and school fight songs blared out by the Cardozo High School marching band. It continued until well past midnight at a City Council public hearing where nearly 100 persons spoke in opposition to the cuts while the Spingarn High School chorus sang spirituals in the hallway outside.

From council members, the crowd got a lot of sympathy but no promises.

Council chairman Arrington Dixon, who crisscrossed the crowd outside carrying a sign that read "Quality Education Needs $$$," reminded the gathering that the council last year came up with an additional $15 million for public schools by cutting the budgets of other city departments. Dixon warned that this time "We will be looking at the taxes that may need to be raised in order to fully fund our schools."

Council member David Clarke (D-Ward 2) told the crowd that the council would search for a way to provide more money for schools, but cautioned parents that they should also make it their responsibility to see that it is spent properly since school officials have autonomy over their budget once it is funded.

School officials had requested $265 million for the school year that begins next September, but the mayor's budget request for fiscal year 1982 proposes only $238 million for public schools.

The tense, and sometimes heated atmosphere outside the District Building continued inside the council chambers, as parents and educators took turns railing against the city government and its elected officials for being too divisive, too bogged down with political infighting, and lacking in the will to make tough decisions.

"I'm tired, I'm tired of all this nonsense about how difficult it is to make decisions," said Peter Edelman, a member of the Parents United group. "You knew before you were elected that you would have to make difficult decisions."

Harold Himmelman, chairman of the Ward 3 Advisory Commission on schools said, "It's unfortunate that a state of war has existed between the mayor, the council, and the board of education. It is shameful that public education has been allowed to become the political football of this government."

Further council action on the budget has not yet been scheduled.