In a move that set off a major inter-union dispute here, striking musicians at the New York City Opera today were urged to return to work immediately by eight other unions at the opera company's home, the New York State Theater at Lincoln Center.

In a move that isolated Local 802 of the American Federation of Musicians, which represents the orchestra players, leaders of the unions for most other unionized employes of the theater--including the singers, stage hands and ticket sellers--appealed to the musicians to give up their strike and to accept as binding the findings of a just-appointed board of inquiry.

The board was appointed today by the New York State Department of Labor.

The strike is in its seventh week and the opera company already has canceled the first two months of its summer season.

The eight unions also asked the opera company management to resume the season and to accept the findings of the inquiry board.

John Glasel, president of the musicians' union, said of the move by the other unions, "I think it stinks.

"It's a great example of union solidarity," Glasel said in sarcastic anger.

He said the musicians will not agree to the request by the other unions and will not cooperate with the board of inquiry.

New York State mediator William J. Glinsman said the state labor department appointed three persons to the board of inquiry: Basil A. Paterson, former New York City deputy mayor and former New York secretary of state;Eric Seif, former New York state commissioner of investigations; and Dan House, a labor arbitration expert Dan House. The administrative secretary of the board will be James J. McFadden.

The opera company said it welcomed the inquiry panel. The company already said it would agree to binding arbitration--effectively the plan called for by the eight unions yesterday.