(The Hill) — Voters in California showed up on Tuesday in support of tough-on-crime policies, while House Republican incumbents across the country fought off primary challenges from their political right.

The primaries in California, Iowa, Mississippi and beyond underscored intraparty divisions among both Democrats and Republicans, while also offering some hints about their prospects in the November general election.

Here are five takeaways from Tuesday’s primaries.

Anxieties over crime draw spotlight

San Francisco residents, weary from rising property crimes and other offenses, voted by a wide, 20-point margin on Tuesday to boot District Attorney Chesa Boudin (D) out of office in a recall election that was seen as a rejection of progressive policies toward crime and punishment.

Boudin, one of the most progressive top prosecutors in the country, used his post in the district attorney’s office to advance a more lenient approach to crime, eliminating cash bail and working to tackle mass incarceration.

But after 2 1/2 years in office, many voters in the famously liberal city rejected Boudin’s policies, signaling a changing sentiment among some Democrats who have grown skeptical of progressive approaches to crime after a pandemic-era spike.

A similar story unfolded in Los Angeles, where billionaire Rick Caruso finished as the top vote-getter in the city’s mayoral race.

While he’ll still have to make it through a November runoff election against Rep. Karen Bass (D-Calif.), the Tuesday vote was seen as a major show of support for a candidate who built a reputation in politics as a member of the Los Angeles Police Commission and vowed throughout his campaign to get tough on crime.

GOP House races underscore splits over Trump, Jan. 6

In Republican House nominating contests from Mississippi to California, GOP incumbents faced primary challengers who sought to cast themselves as unequivocally loyal to former President Trump.

The results in many of those races suggest that GOP voters remain divided over how important that loyalty is.

In Mississippi, Rep. Michael Guest was forced into a June 28 primary runoff against Michael Cassidy, who attacked Guest as insufficiently loyal to Trump. Guest was one of 35 House Republicans who voted last year for the creation of an independent commission to investigate the Jan. 6, 2021, riot at the U.S. Capitol. 

Likewise, South Dakota Rep. Dusty Johnson, who also voted for the Jan. 6 commission, faced a primary challenge from state Rep. Taffy Howard, who had the backing of a pro-Trump super PAC that has pushed the former president’s claim that the 2020 election was stolen from him.

Johnson, South Dakota’s lone representative in the House, ultimately overcame that challenge, winning nearly 60 percent of the vote. Still, the race highlights how many Republican voters are torn between loyalty to the former president and more traditional conservatives.

Democratic voters shift toward political center

If the marquee races in California showed anything, it’s that voters in the heavily Democratic state may be tiring of the progressive policies that many of them once pined for.

Caruso’s top finish in the Los Angeles mayoral race, for instance, handed a victory to a former Republican who vowed tackle the city’s challenges with crime and homelessness.

In San Francisco, the decision to remove Boudin from office signaled a deepening malaise among voters with progressive approaches to criminal justice just two years after the murder of George Floyd sparked a national outcry for police reforms.

Even California’s progressive attorney general, Robert Bonta (D), who advanced to the general election on Tuesday, sought to emphasize his commitment to tackling crime after facing attacks from challengers accusing him of being soft on the issue.

The results out of California — one of the bluest states in the country — suggest that many Democratic voters may be seeking a return to the political center at a time when progressives are hoping to expand their footprint within the party.

A once-rising star goes down in Iowa

On paper, former Rep. Abby Finkenauer (D-Iowa) appeared to be a shoe-in for the Democratic Senate nomination in Iowa. She was among the candidates who helped Democrats reclaim their House majority in 2018, maintained a strong fundraising pace and racked up endorsements from current and former Democratic officials.

Iowa voters ultimately went in a different direction.

Finkenauer lost the Tuesday primary to retired Navy Adm. Mike Franken, who sought the party’s Senate nomination in 2020 and has never held elected office before.

Franken cast himself as the kind of candidate who could court both independent voters and more centrist Republicans. And in the months leading up to the June 7 primary, there were signs that his message was paying off. He outraised Finkenauer in both of the last two fundraising periods and heavily outspent her on advertising.

The primary results illustrate a remarkable downfall for Finkenauer, the kind of Democrat who once appeared to have a promising future within the party. Her defeat on Tuesday was her second in less than two years; she lost reelection in 2020 to Rep. Ashley Hinson (R).

California turnout flashes warning signs for Democrats

It’s easier than ever to vote in California. The state sends every registered voter a mail ballot and the postage is pre-paid, meaning voters don’t have to bother with stamps. Drop boxes are readily available, and the state allows for same-day voter registration.

Ultimately, those measures didn’t do much to drive out turnout in the overwhelmingly Democratic state.

According to the California-based firm Political Data Inc., only about 4.1 million of nearly 22 million ballots were returned to election officials — a rate of about 19 percent.

While there may be several explanations for the low turnout — there were few, if any, major races at the top of the ticket in California, and primaries tend to have lower rates of participation anyway — it’s likely to feed into speculation that Democratic voters simply aren’t motivated in 2022.

Given the tough political landscape for Democrats this year, the party can’t afford to lose any of their voters to indifference in November.