Not long after the state issued a new law requiring all students be vaccinated before starting kindergarten, the Lagunitas School District held a meeting with parents to talk over the mandate.

Superintendent John Carroll was braced for a fierce backlash. For years, hundreds of parents in the Marin County district’s two schools had been using a state-sanctioned loophole to opt out of vaccinating their kids. With that loophole now closed, Carroll worried that parents would be scared or angry. He wondered if they would pull their kids out of his schools.

But at that meeting, in the summer of 2015, he was surprised to find that most parents were willing to start vaccinating their children — right away, and with no complaints. The handful of parents who remained strongly opposed, he learned, were finding ways around the legislation. No one was leaving the district.

The result: Vaccination rates shot up. Three years ago, fewer than half of students starting kindergarten in the Lagunitas district were fully vaccinated. At the start of the 2015-16 school year — before the state law even took effect — more than 90 percent were.

“I think we navigated that pretty well,” Carroll said last week, a smile in his voice. “What we all recognized about each other is we all want what’s best for our kids. We all want them to be safe and healthy.”

Lagunitas is emblematic of a trend taking shape all over California in the wake of a massive public policy push to improve the state’s childhood vaccination rates. Even in Marin County, long a sanctuary for parents hesitant about or dead-set against vaccinating their children, immunization rates are soaring.

Over just a few years, California has reversed a trend of falling vaccination rates that had been causing stark fear among public health and infectious disease experts, who warned that parts of the state were becoming vulnerable to diseases like measles and whooping cough.

After a January 2015 measles outbreak that seemed to confirm their worst concerns, new laws and focused efforts by counties and school districts to increase vaccinations had an almost immediate impact. In 2016, the state vaccination rate rose to 95.6 percent, the highest level in more than 16 years, according to a public health report released earlier this month.

In Marin County, the rate climbed to 93.2 percent — a 9-point increase in two years, and 15 points above the low just five years ago.

“We’ve been vulnerable to outbreaks of preventable diseases in Marin County for more than a decade. We’ve had some of the lowest vaccination rates in the state,” said Dr. Matt Willis, the Marin County public health officer. “This is obviously great news.”

But amid the overall improved numbers, pockets of stubbornly antivaccination sentiment remain. In sleepy Modoc County, tucked into the border of Oregon and Nevada, only 79 percent of kindergartners were fully vaccinated in 2016. Seven other counties have rates under 90 percent, too low to offer the so-called herd immunity that prevents infectious diseases from getting a toehold in a community.

In Marin County, though the overall vaccination rate has climbed dramatically, clusters of parents are still finding ways to opt out of immunizing their children. Medical exemptions increased almost ninefold in 2016.

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Before the new state law took effect, parents could apply for a personal belief exemption, which allowed them to not vaccinate their children for any reason. The law removed that exemption. But it kept in place medical exemptions, which typically are for severely immune-compromised children — often, those with cancer undergoing chemotherapy — who cannot safely be vaccinated.

In Marin County, eight incoming kindergarten students had medical exemptions in 2015. The next year, 68 did. There’s no way, public health experts said, that pediatric cancers or other immune-weakening conditions climbed that much in one year.

Indeed, at his meeting with Lagunitas families, Carroll said some parents firmly opposed to vaccinating asked about medical exemptions. A doctor stood up, Carroll recalled, and volunteered to write exemptions for anyone who wanted them, no questions asked.

“He said very clearly that he’d write medical exemptions for anybody. He said, ‘I’ll be writing them hand over fist,’” Carroll said. He couldn’t remember the name of the doctor.

That’s not how the law is supposed to work, said public health officials. Later this year, the state will release vaccination data for specific schools, which should show where parents are relying heavily on medical exemptions to keep their children in school. When those reports come out, some public health officials said they’ll likely be following up with schools, parents and doctors.

At several Bay Area schools that have had exceptionally high rates of children with personal belief exemptions, officials refused to comment or did not return phone calls in reference to how parents were coping under the new law.

But public health officials said those parents are a small minority now. In fact, what school and public health authorities realized in the aftermath of the measles outbreak and the resulting legislation was that most parents who hadn’t been getting their kids immunized weren’t necessarily strongly antivaccination.

Instead, they were more vaccine-hesitant, said Dr. Oded Herbsman, vice chair of pediatrics at San Francisco’s California Pacific Medical Center. Parents were confused and concerned, he said.

They’d heard about an association between vaccines and autism — a connection long ago debunked — and maybe read other unsubstantiated reports online about the so-called dangers of childhood immunizations. Weighing the threat of a disease like measles, which they’d never seen or experienced, against the fear that vaccines could cause autism, they chose to not vaccinate. And the state made it easy.

“There was so much doubt out there and so much wrong information,” said Herbsman. “I’m a parent too, and if I saw something and all I remembered was that my child could get autism, yes, I see how that happens. It’s hard to unsee certain things. But they were playing Russian roulette.”

Then the measles epidemic hit. It started at Disneyland and ultimately infected more than 130 people in California, most of them not vaccinated. A long-simmering debate around vaccinations became loud and heated.

And for many parents who had been vaccine-shy, the balance of perceived threat shifted. Parents who thought they were erring on the side of caution by not getting their kids vaccinated reconsidered.

“It was a mental switch for a lot of people, in a very good way,” Herbsman said.

Few places were more directly affected by that change of heart than Reed Elementary School, a pretty campus of pastel-colored buildings tucked into a Tiburon hillside overlooking San Francisco Bay.

At the start of the 2013 school year, 15 percent of kindergartners there were not fully vaccinated. Ten of those 27 children weren’t vaccinated because their parents chose not to. One child, Rhett Krawitt, was unable to get vaccinated because he’d had leukemia and his immune system wasn’t strong enough.

When the measles epidemic hit, Rhett’s parents were told that their son might have to stay home if measles was discovered in the community. He was too vulnerable to illness, school officials said. Rhett’s family fought back — why should he have to miss school when his peers were the ones putting him at risk by not being vaccinated?

Over the next few months his family spoke out publicly at school board and county supervisor meetings, in the media, and eventually in Sacramento, blasting families for choosing not to vaccinate. When state Sen. Richard Pan, D-Sacramento, proposed the legislation banning personal belief exemptions, the Krawitts happily made Rhett a poster child.

They faced some criticism from parents strongly opposed to vaccination, said Carl Krawitt, Rhett’s father. But mostly, other parents supported them.

At Reed Elementary, suddenly a focal point for what had become a state dialogue around vaccinations, immunization rates improved almost immediately. Less than a year after the measles outbreak, the number of children not vaccinated was cut by more than half.

“There was this outpouring of support,” Carl Krawitt said. “The measles outbreak was a wake-up call for most people. It wasn’t just about taking care of yourself and your family. It was about taking care of the community.”

Erin Allday is a San Francisco Chronicle staff writer. Email: eallday@sfchronicle.com Twitter: @erinallday