Half of Californians support the travel ban on Muslim-majority countries and 59% are in favor of increased deportations, according to a new survey that suggests there are widespread conservative and xenophobic views in one of the most progressive US states.

The poll, conducted by the University of California, Berkeley, found that while a majority of Californians say they broadly support immigrants’ rights and refugees, many also back signature features of Donald Trump’s anti-immigrant agenda in a state that has served as the leader in opposing the president’s policies.

“In this period when immigrants are being attacked, Californians felt that it’s important to increase deportations,” said Olivia Araiza, the director of the Haas Institute’s Blueprint for Belonging Project, which commissioned the survey alongside the polling group Latino Decisions. “Even Californians are sensitive to rhetoric that excludes people.”

The poll was released at a time of intensifying disputes between the Trump administration and the Golden State, which is home to more than 2 million undocumented people, nearly a quarter of all unauthorized immigrants in the US. Last year, the state passed a landmark “sanctuary” law meant to limit local police cooperation with federal immigration authorities, sparking a US justice department lawsuit and mass arrests and raids.

While the state’s urban centers like San Francisco and Los Angeles are known as liberal havens, there are some signs of rightwing rage brewing in certain conservative regions under Trump.

Araiza emphasized that the results of the survey of 2,440 residents (conducted in English and Spanish in December) were largely pro-immigrant. The poll found that 71% think establishing a pathway to citizenship is important, 79% support citizenship for Dreamers, undocumented people brought to the US as children, 64% agree the state should limit local cooperation with federal immigration enforcement, and 66% reject Trump’s US-Mexico border wall as an important immigration policy.

The US-Mexico border fence cuts through Jacumba, California. Two-thirds of those polled do not see the border wall as an important policy. Photograph: Sandy Huffaker/AFP/Getty Images

While 79% also said they think it’s important to take in immigrants and refugees escaping war and violence, the number fell to 66% when Muslim-majority countries were specified, and 49% said they support Trump’s travel ban. Only 54% said they have “positive views” of Muslims.

“People hold inconsistent and contradictory points of views at once,” said Araiza, adding, “We have a job to do to ensure that we use any pulpit we might have to steer people toward belonging and inclusion.”

Trump and his attorney general, Jeff Sessions, have argued that a crackdown on immigrants prevents violent crime, but numerous studies have contradicted that narrative – finding that cities with sanctuary policies have significantly lower crime rates and that undocumented immigrants are less likely to commit serious crimes than people born in the US.

The survey also found contradictory views about race and prejudice. While 68% of respondents said they support race-conscious policies like affirmative action, about half said they agreed with the racist idea that black people need to “try harder”.