State Assemblywoman Catharine Baker is a rare bird: a living, breathing Bay Area Republican elected representative in a sea of Democratic blue.

So at a time when town halls hosted by GOP politicians around the country have become the go-to venue for unleashing fury on the Trump administration and its policies, you would think that a Baker town hall would attract at least a bit of that wrath and protest.

But that was not the case at San Ramon City Hall on Thursday night.

In a display of bipartisan civility not seen much these days, Baker, the Republican from San Ramon, and Democratic State Sen. Steve Glazer of Orinda joined forces to give their Tri Valley constituency the latest news from the state Capitol. With more than 300 people in attendance — half of them watching on a screen in the building’s rotunda — the political odd couple of Contra Costa County talked about higher education, infrastructure, transportation, water storage, transgender rights, BART, high speed rail, health care and DNA testing.

What they didn’t talk about, at least directly, was the man who could have a dramatic impact on all those issues: President Trump. Baker said that while attendance at her town hall meetings has doubled since Trump was elected, her constituents don’t seem to hold her responsible for what comes out of Trump’s mouth and administration.

“I don’t think you saw any of that here,” Baker said afterwards. “The real focus here is on exactly what it should be: what should we be doing, regardless of party, to improve the lives of people in this community. It’s not ‘are you toeing the line? What does your party say about this or that?’”

Republicans, with the exception of Baker, have not done well in the Bay Area over the last decade. The state Senate has 27 Democrats and 13 Republicans, but no Republicans from the Bay Area. The Assembly is made up of 55 Democrats and 25 Republicans, and only one, Baker, is from the Bay Area. None of the 14 California Republicans in the U.S. House of Representatives is from the Bay Area.

And even in her own district, Baker is a minority. Republicans make up just 31 percent of her 16th Assembly District, compared with 39 percent Democrats. Trump got trounced in Contra Costa County, which covers much of the district, garnering 24.5 percent of the vote, compared with 67.5 for Hillary Clinton.

It might have helped that Baker did not endorse Trump and condemned him after audio tapes surfaced in which the president was heard bragging that he forces himself on women. “I took a stand early and publicly not to support Donald Trump, and it lost me supporters,” she said at the time. “The most recent revelations of his taped statements about women re-affirm my stance not to vote for Trump. As a mother and a woman, I find his statements disgusting.”

But while Glazer and Baker have different party affiliations, they agree on most things. Of the 1,210 bills that made it to both the Assembly and Senate for votes in 2016, Glazer and Baker voted the same 88 percent of the time. They both are unpopular with teachers unions because they support charter schools. They are both on the outs with BART workers because they think public transportation workers, like police officers and firefighters, should not be able to go out on strike.

“Transit is an essential service — it’s not a luxury,” said Glazer at the town hall.

They both said they want infrastructure investment, but not waste. They both said high speed rail between San Francisco and Los Angeles is a waste of money. They both back Baker’s legislation that would ensure that BART bond money is spent on system capital improvements, not administrative costs.

“If we are taking money from you in the name of transportation, it needs to go to roads and infrastructure,” Baker told the audience.

Perhaps out of politeness, audience members seemed to tread lightly around Baker’s affiliation with the party of Trump. She was asked about the likely dismantling of the Environmental Protection Agency’s greenhouse gas reduction efforts by new EPA head Scott Pruitt.

“I was one of the only members of my party to support climate change and greenhouse gas reductions standards,” she said. “We need to blaze ahead ourselves as best we can.”

In another break with the Trump administration, Baker also said she supports the right of transgender people to use whatever public facilities they feel comfortable using.

Several attendees showed up with signs that revealed their anti-Trump positions. Peggy Kroll of Danville had a sign saying “Invest In People Not Jails.” Connie Chilba of Moraga held a sign in support of Senate Bill 54, the “California Values Act,” which would prevent local and state public resources from aiding federal Immigration and Customs Enforcement in deportation actions.

Chilba said she was “very concerned about the hate and fear we are living under” and appreciated the bipartisanship Glazer and Baker had on display. “This kind of reaching across the aisle is an example for the rest of the county.

The joint town hall was the eighth in a series, and Glazer said they would keep doing them.

“Our political world is getting pretty polarized,” said Glazer. “It seems like people are getting in their corners and are more interested in fighting than finding common ground.”

J.K. Dineen is a San Francisco Chronicle staff writer. Email: jdineen@sfchronicle.com

Twitter: @SFJKDineen