With choruses of polite applause and occasional boos, about 300 Alexandria residents told their City Council last night how they felt about a proposed "teen clinic" that would distribute contraceptives to students at the city's high school.

Dozens of clinic supporters and opponents went before the council and the Alexandria School Board during a long public hearing that was accompanied by unusually tight security measures. Fire marshals and plainclothes police officers patrolled the halls outside the 150-seat council chamber in City Hall, while the overflow crowd watched on television monitors throughout the building.

The clinic, which would be near T.C. Williams High School and would be the first public facility of its kind in the Washington area, has prompted a strong emotional response on each side. Though no action was taken on the proposal last night -- the School Board is scheduled to vote on a resolution endorsing the clinic tomorrow and the council plans to act next month -- the intensity of feelings was obvious.

"Were this proposal merely an excuse for an expensive contraceptive vending machine, I would oppose it," said Rabbi Jack L. Moline. But he said the clinic would provide many medical services, including birth control advice, to students who could not otherwise afford it. Moline urged the council not to cave in to "a vocal minority who demand that their standards be met."

Msgr. Francis L. Bradican spoke on behalf of the Catholic Diocese of Arlington, which includes most of Northern Virginia, saying, "What we cannot condone is the dissemination of birth control devices and information {at the clinic}. This puts the schools in the position of giving tacit approval to premarital sex."

Although detractors of the clinic appeared to outnumber advocates at the hearing, the few students who spoke endorsed the facility. "Whether parents want to think so or not, everyone {at T.C. Williams} is having sex," said Gina LaSasso, a student. "It's not just the poor kids or the kids with a sleazy reputation. The clinic is saying, 'Don't have sex. But if you're going to have sex, use contraception.' "

Whether or not the clinic is built, it is expected to be an issue in city elections in May. Last night, about a dozen anticlinic demonstrators carried signs outside City Hall that read "Teach our children, don't corrupt them" and "Moran's folly." Mayor James P. Moran Jr. has been an outspoken supporter of the clinic.

The controversy over the clinic picked up steam this fall when state health department statistics showed that Alexandria's 1986 teen-age pregnancy rate was the highest in the state. Last week, clinic opponents spent $7,500 on radio and newspaper ads, while advocates mounted a smaller campaign.

The Catholic Church served as a rallying point for the clinic's detractors. The Diocese of Arlington issued a statement opposing the facility, and all of Alexandria's Catholic churches asked for prayer on the issue in masses Sunday, Monday and Tuesday.

Alexandria schools have for several years taught a nationally recognized sex education curriculum. Students can already get contraceptives and birth control advice through the city Health Department, which operates a clinic across town from T.C. Williams. And a half-mile from the school, a nonprofit clinic in a Methodist church offers the same services.

But the explosive nature of the issue brought powerful emotions to the surface. "I stand in amazement to hear repeated references to pregnancy as if it were a virus that affects innocent bystanders," said the Rev. Louis M. Gonzalez of the Alexandria Church of God. "It happens to teen-agers who have sex."