The upcoming California election has it all. Heated rhetoric. Mudslinging. A last-minute celebrity candidate who shakes up the field.

This isn’t the gubernatorial recall. It’s the race to become president of powerful Hollywood labor union SAG-AFTRA.

Fran Drescher

The contest pits actor Matthew Modine, whose credits include the Netflix hit “Stranger Things,” against onetime sitcom star Fran Drescher. Mr. Modine’s camp casts him as underdog to the bigger name, though Ms. Drescher is best known for her role in “The Nanny,” which aired its final season in 1999. Her most recent acting credit was a supporting role as a widow in a Christmas movie that aired last year on the Lifetime cable network.

“Unfortunately many of our members are more impressed by a candidate’s IMDB page than they are by a candidate’s position on union issues,” says actress Anne-Marie Johnson, a supporter of Mr. Modine.

SAG-AFTRA represents 160,000 performers—ranging from movie stars to background actors and stunt performers—and both candidates have recognizable names in their corners, according to public statements of support. Ms. Drescher, 63, was endorsed by actors including Tom Hanks and Rosie O’Donnell. Mr. Modine, 62, boasts backing from Whoopi Goldberg and Diane Keaton, as well as former “The Nanny” co-stars Charles Shaughnessy and Madeline Zima. The Baldwins are split; Alec favors Ms. Drescher, while younger brother Billy is behind Mr. Modine.

The candidates are vying to succeed Gabrielle Carteris, who played brainy high school newspaper editor Andrea on the 1990s hit “Beverly Hills 90210.” Ms. Carteris, who has led the organization since 2016, urged Ms. Drescher to run, according to the latter. The post has a storied history— Ronald Reagan got his start in politics as SAG president.

After qualifying for the race last month in the final hours before eligibility ended, Ms. Drescher immediately stole the spotlight. Two days later, Vanity Fair published an article headlined, “Fran Drescher Will Run to Form a More Perfect and Glamorous Union.” The article asked, referring to Ms. Drescher and her running mate, actor Anthony Rapp : “Why are they running to lead SAG and not the White House?”

Fran Drescher, right, is famed for her role on ‘The Nanny.’

Photo: CBS/Everett Collection

Those opposed to Ms. Drescher’s candidacy point to the ticket’s lack of experience with the union. “They have never been in the [SAG-AFTRA] building,” says actress Joely Fisher, running to be secretary-treasurer under Mr. Modine.

Ms. Drescher has also been on the defensive for public remarks suggesting that 5G wireless service causes cancer and spreads Covid-19, and that she was abducted by aliens as a child.

In a written response to questions, Ms. Drescher stood by her 5G concerns. “It behooves us to question why we get sick and how to boost our immune systems,” she wrote.

Regarding extraterrestrials, she wrote, “I won’t dignify the alien question with an answer. I’m surprised at you!”

As qualifications, Ms. Drescher cites her experience as founder of the nonprofit Cancer Schmancer and describes herself as an action-oriented outsider. “I want our more famous members, more ‘glamorous’ if you will, to be more directly involved and excited by the union, to integrate their expertise and compassion for common goals,” she wrote.

As she put it in a campaign video: “I’m a celebrity that goes to the mat over and over again for the greater good.”

The latest controversy is an August interview of Ms. Fisher by a Los Angeles television station. Current SAG leadership determined it violated campaign rules because the opposing camp didn’t receive equal time (the interviewer said on-air that Ms. Drescher’s side was welcome to appear).

In an Aug. 26 email to union members, Ms. Drescher wrote, in reference to the interview, that Mr. Modine and his ticket “think it’s okay to violate the law and that the rules don’t apply to them.”

Mr. Modine responded the same evening during a virtual town hall that he was “ashamed of Fran Drescher.” Her email was “slanderous and hateful and hurtful, not just to myself in my life, but to my career,” Mr. Modine wrote.

Matthew Modine, right, appeared with Michelle Pfeiffer in the 1988 film ‘Married to the Mob.’

Photo: Orion Pictures/Everett Collection

The race isn’t polled, and it’s unclear who is favored. Voting began earlier this month and a winner will be announced on September 2. In 2019, only 21% of eligible members voted, according to union data.

Behind the sniping are some serious issues. SAG-AFTRA was formed after the 2012 merger between the Screen Actors Guild and the American Federation of Television and Radio Artists. The organization negotiates with several factions of the entertainment industry, including the Alliance of Motion Pictures and Television Producers, which makes deals on behalf of studios, networks and streaming services.

Mr. Modine, who is making his second run for union president, wants to overhaul the organization. He says it has become too soft, particularly in regard with new forms of media, with the industry that employs most of its members.

Mr. Modine says the union was wrong to accept a deal that lowered payments to members for television reruns by $70 million over the next three years. “You don’t give away things you own unless they are going to give you something that is better,” Mr. Modine says.

The next administration will also have to contend with a recent restructuring of the union’s healthcare plan. Some 12,000 members—mostly senior citizens—lost coverage, leading to lawsuits alleging age discrimination. The union says the changes were driven by pandemic-related budget cuts.

While the acrimony between the two presidential tickets is thick, some candidates lower down on the ballot treat the contest with less gravity. “Curb Your Enthusiasm” co-star Jeff Garlin, running for vice president of the Los Angeles union chapter, lists his official candidate statement as: “A vote for me is a vote for Jeff Garlin.”

Write to Joe Flint at joe.flint@wsj.com