A proposal to impose a 5 percent District of Columbia sales tax on theater admissions and a variety of services industries encountered strong opposition yesterday from two dozen witnesses at a D.C. City Council hearing.

John A. Wilson (D-Ward 2), chairman of the council's finance and revenue committee, said after several witnesses testified that he would be willing to drop the proposed taxation on nonprofit theatres, including the John F. Kennedy Center for the Performing Arts.

Under the bill, on which no action was taken, the tax would be imposed on now-exempt items including laundry, dry cleaning, barber and beautician services and fees collected by private employment agencies, credit and collection agencies, interior designers and private detectives as well as on theater admissions.

Everett A. Bergmann Jr. of Bergmann's Laundry said the proposal would decrease business in the city and add to unemployment.

Wilson warned that the city must raise funds to close the gap between future tax income and municipal expenses.

Even before a House subcommittee recently voted to reduce the annual federal payment to the city - an action still pending - Wilson had estimated that the city would enter the 1981 fiscal year with a gap of $104 million between projected income and outgo.

City tax officials estimated yesterday that the broadened sales tax would increase revenues by at least $4.3 million a year.