“This is a little family business that’s been in Times Square since 1995, when Times Square was still a toilet, and we give these guys the opportunity to ply their craft in the middle of the theater district to sing,” he said. “I welcome and have always welcomed the opportunity to make their life a little bit better, because it’s a brand, and at the end of the day, you’re only as successful as your employees.”

The difficulties began in January, according to a half-dozen servers and a letter sent to Mr. Sturm by the union, Stardust Family United. Mr. Sturm hired several new managers who pledged a better-run, more streamlined way of delivering egg creams and musical numbers. What happened instead, the workers said, was a mass firing of longtime servers, many for small offenses or ones seemingly beyond their control. Last week, for example, a waitress was fired when a table of customers left without paying, Ms. Bogan and others said.

Servers at Ellen’s are known as Stardusters, and their head shots grace the diner’s walls and website like celebrities in a playbill. But behind the scenes, workers said, the new managers warned them that they were easily replaceable. When employees complained about a new scheduling system that prevented them from switching shifts so they could make it to auditions — the point, many said, of working at Ellen’s — they were derided as divas.

“Stardust was basically our home,” said Brian Esposito, 23, a waiter known for renditions of songs from the musical “Hamilton.” “You always felt safe coming there; it was a community of artists. But now, so many people, some who have been there for five-plus and 10-plus years, they walk in and they’re crying in the back hallway.”

Marianne LeNabat, an organizer with the Industrial Workers of the World, a union that helped guide the servers through the process of organizing a union, said she was stunned by the situation at Ellen’s.

“I’m actually kind of shocked when they tell me what’s going on in that workplace and especially because it’s the kind of place where the staff is really, really dedicated,” she said. “A lot of workplaces throw the word ‘family’ around, but these workers really think of each other as family.”