The Met, whose pre-pandemic annual budget was slightly above $300 million, is moving ahead with plans for a 2021-22 season, but it must first contend with some harsh financial realities. A key factor is the loss of $150 million in revenue because of the pandemic, according to the company. That has left the Met seeking pay cuts from its 2,500 union employees. Labor costs account for $200 million of its budget, according to the Met.

The Met is also facing the question of whether audiences will feel safe returning to indoor venues. The problem is compounded by its theater’s 3,800- seat capacity, which is about double that of Broadway’s largest space.

Adding to the Met’s concerns are questions in the cultural community about whether opera, a centuries-old art form with white, European roots, is one that can effectively speak to contemporary America, particularly in the wake of the murder of George Floyd in police custody and the Black Lives Matter movement.

The Met had financial challenges before the 2020 shutdown, and there was also the severing of its relationship with the longtime conductor James Levine as he faced allegations of sexual abuse. Mr. Levine died in March.

“For years, people have been saying the Met has to rethink its vision and operating model, and that was before the pandemic,” said Richard Mittenthal, a Met subscriber and president and chief executive of TCC Group, a New York City-based consultant to nonprofit organizations. “This has just raised the stakes.”

The Met said it is tackling the issues it faces and has a season ahead filled with new productions. Among them are company premieres of three contemporary works, including Terence Blanchard’s “Fire Shut Up in My Bones,” the first opera by a Black composer that the company has ever presented. Mr. Blanchard’s work opens the season on Sept. 27, though the Met is also planning a performance of Verdi’s “Requiem” on Sept. 11 in connection with the 20th anniversary of 9/11.

The company’s negotiations with unions representing its various employees could be the biggest hurdle it has to overcome. The Met said it is hoping to save the equivalent of 30% of payroll costs from its highest-paid unions, though the company adds that the impact on take-home pay would be roughly 20%.

The Met has an agreement awaiting union ratification with the American Guild of Musical Artists, which represents choristers and vocal soloists, among other employees. AGMA officials said the new contract would result in an initial pay cut of 3.7% for much of the represented employees.

That still leaves the International Alliance of Theatrical Stage Employees Local One, the stagehands union, and the American Federation of Musicians Local 802, which represents orchestra members and other music personnel. The Met locked out its stagehands in December after a period of labor negotiations.

IATSE Local One President James J. Claffey Jr. has questioned the severity of the company’s financial situation. “The Met shouts about a $150 million loss in revenue but is conveniently quiet about the savings accrued by not paying expenses associated with the production of the opera,” he said.

Mr. Claffey disputed the Met’s statement that the proposed pay cuts would result in a 20% decrease in take-home pay. He said the reduction would be higher.

The Met said it hopes to resume negotiations with stagehands soon.

AFM Local 802 President Adam Krauthamer said the Met musicians are among the highest-trained and most-experienced in the world and shouldn’t be faced with what he described as disastrous cuts.

The Met said it would aim to restore half of its proposed pay cuts with unions when its ticket sales and donations return to pre-pandemic levels.

The company is also looking at what it can do to reassure its audience members when many might worry about being back in indoor environments. Among the steps it is taking is installing touchless doors, restrooms and ticketing.

The company said it is focused on diversity beyond the presentation of an opera by a Black composer and commissions of works by other artists of color. In January, the Met announced the appointment of its first chief diversity officer, Marcia Lynn Sells.

“We need to create artistic and administrative pathways for people of color to achieve equity among our artists and artisans and for all of our employees and members of our board,” Met General Manager Peter Gelb said at the time of the appointment.

Write to Charles Passy at cpassy@wsj.com