SAN FRANCISCO — Robert Dunne tried hard to live like a man. He got a job in heavy construction and became a skilled sheet-metal worker. He got married--three times. But for nearly 30 years, he knew he wasn't being true to himself.

Finally, he decided to have a sex change operation, but when word leaked out at his workplace, he found himself without a job. Now Robert has become Roberta, and the onetime hermit has blossomed into an activist fighting discrimination against transsexuals and cross-dressers.

Through the efforts of Dunne and others such as her, San Francisco is on the verge of enacting the toughest law in the nation aimed at protecting the city's transgender community from discrimination in employment and housing.

Approved by the San Francisco Board of Supervisors this month, the ordinance would add "gender identity" to the list of categories such as race, age and HIV status already protected from discrimination under city law. Mayor Frank Jordan is expected to sign the measure this week, and its euphoric supporters say that the idea soon will spread nationwide.

"It's not just a San Francisco thing," Dunne said. "This is an extremely important problem we're presenting to the whole country. We are educating people that we are like everyone else."

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San Francisco, with a long tradition of tolerance, was among the first in the nation to outlaw discrimination against homosexuals and people with AIDS. But transsexuals and cross-dressers say they have continued to suffer harassment--some of it violent.

The new law would embrace a wide variety of people: transsexuals (whether or not they have had sex change surgery), cross-dressers (the preferred term for transvestites) and hermaphrodites (people born with both male and female sexual organs).

Supporters estimate that the ordinance will cover about 6,000 of San Francisco's 724,000 residents.

"We are calling for an end to hatred, to abuse, to disrespect," said Jamison Green, director of FTM International, an association of transsexuals. "We are calling for the right to define ourselves, to say for ourselves who we are."

Although the San Francisco Chamber of Commerce has taken no stand on the measure, some business owners are outraged. They worry that it will force them to employ workers they consider undesirable.