The Supreme Court, acting in a case that could have great impact on the cable television industry, agreed yesterday to decide whether constitutional rights to free speech limit the power of cities to regulate cable operators.

The justices will review a California federal appeals court ruling last March that the First Amendment prohibits the city of Los Angeles from awarding an exclusive cable television contract to one cable company. As long as the city has the facilities to accommodate more than one cable company, the court said, it must do so.

"Allowing a procedure such as the city's would be akin to allowing the government discretion to grant a permit for the operation of newspaper vending machines located on public streets only to that newspaper that the government believes 'best' serves the community," the appeals court said.

The high court's action comes as Congress, the Federal Communications Commission and the courts are moving to deregulate the cable industry. The California ruling was the first time an appeals court had declared specifically that cable companies have First Amendment rights similar to those of newspapers.

Cable operators had in the past been treated more like radio and television broadcasters for purposes of regulation. Governments can regulate broadcasters because there is a technological limit to the number of signals that can be transmitted.

Newspapers are free from such regulations, because technology does not limit their numbers. Cable operators, the California court said, are like newspapers. The court struck down Los Angeles' system for selecting a single company to operate the city's system.

A ruling in the case, Los Angeles v. Preferred Communications, is expected this spring.

The court, adding a fifth case involving church-state separation to its docket, agreed yesterday to decide whether states may enforce sex discrimination laws against a fundamentalist Christian school that fired a pregnant teacher.

The case, Ohio Civil Rights Commission v. Dayton Christian Schools Inc., began after the school refused to renew the contract of a teacher, Linda Hoskinson, because the school's policy was "to have a mother home with preschool-age children."

When Hoskinson contacted a lawyer to challenge the decision, she was fired because she failed to follow the "biblical chain of command," which the school said called for differences to be resolved within the church.

Hoskinson filed a charge of sex discrimination with the Ohio Civil Rights Commission. The 6th U.S. Circuit Court of Appeals blocked the commission from investigating.

The court said an investigation and enforcement of the law would violate the school's First Amendment guarantee to freedom of religion. The appeals court said the Ohio Civil Rights Act would force the school to reinstate a teacher fired for religious reasons and would unconstitutionally entangle the state in church matters.

In other action yesterday, the court:

*Said it would consider whether the Fifth Amendment's protection against self-incrimination, ordinarily invoked in criminal proceedings, covers someone facing civil commitment to a mental institution. The case involves Illinois' "Sexually Dangerous Persons Act," which allows indefinite confinement of those found to be sexually dangerous.

The court's decision in Terry v. Illinois could affect similar rulings in at least four other states, including Maryland.

*Agreed to hear an appeal (Arcara v. Cloud Books Inc.) by Erie County, N.Y., prosecutors who want to close an adult bookstore that allegedly allowed sexual activities to occur inside. A state court ruled that the prosecutors could not close the store without violating the owner's First Amendment rights.

*Agreed to decide whether a state may pay black employes less than white employes for the same work so long as the pay differences resulted from actions taken before passage of the 1965 Civil Rights Act.

The cases, Bazemore v. Friday and U.S. v. Friday, find the Reagan administration and the NAACP Legal Defense and Educational Fund Inc. -- normally at odds -- on the same side. Both are arguing that the North Carolina Agricultural Extension Service discriminates against its black extension agents. About 50 agents sued in 1971, claiming that they were paid about $1,000 a year less than whites for the same work because of illegal separate pay systems that had been in force before passage of the federal civil rights laws.

A divided appeals court in Richmond said the different pay scales for pre-1965 workers could continue.

The fund also seeks to have the high court overturn the appeals panel's endorsement of a "freedom of choice plan" to desegregate state-sponsored 4-H and homemaker's clubs.