Uber and Lyft, companies worth billions of dollars, have decided to take their ball and go home, “pausing” operations in Austin, Texas, to protest city regulations that their drivers must submit to fingerprint background checks.

The companies’ pullout has cut off a vital source of income for thousands of drivers, and leaves passengers stranded as well.

“It seems like a petulant, childish response: We didn’t get what we want so we’ll do this,” said Veena Dubal, associate professor of law at UC Hastings, who studies ride-service drivers. “But it’s a brilliant business strategy — and really disturbing at the same time.”

The very fact that the two companies felt empowered to follow through on threats to leave Austin if voters didn’t loosen its ride-hailing rules underscores how entrenched they’ve become.

“It says a lot about the power of these companies that they’re willing to pull out of a major city over this,” said Edward Walker, a UCLA sociology professor and author of “Grassroots for Hire.” “They seem to be playing the long game; I doubt they’re giving up Austin forever.”

Dubal agreed.“They’re working off being so popular among consumers, so zeitgeist in the world of transportation that Austin cannot live without them,” she said. “They’re banking that they can drum up enough discontent among the citizenry of Austin that they’ll be asked back on their own terms.”

Indeed, that very scenario has played out in other areas where lawmakers tried to clamp down on the upstart ride services. Last summer, both pulled out of Broward County, Fla., to protest “onerous” regulations, only to return a few months later after County Hall caved in to public backlash, and removed rules the services objected to.

Closer to Austin, they temporarily ceased operations in San Antonio last year over an “impossible” regulatory climate, but were back within months.

“We did pause operations in San Antonio when the city passed an ordinance mandating fingerprinting, but the community spoke out in support of bringing ride-sharing back, and we were able to work with the city to find a solution,” said Lyft spokeswoman Chelsea Wilson. “The council passed a revised ordinance that did not include mandatory fingerprinting, and we were able to return last December.”

Both Uber and Lyft excel at harnessing ordinary citizens — riders and drivers — to lobby lawmakers on their behalf. They’re able to unleash swarms of emails, petitions, rallies and tweets from regular folks to speak for them, following a playbook that political observers say is both sophisticated and effective.

Austin actually showcased a rare political failure. The companies ponied up close to $9 million to try to persuade Austin voters to overturn the city’s tough ride ordinances (besides fingerprint checks, it has requirements for data reporting and vehicle identification), but lost on Saturday by a margin of 56 to 44 percent. That triggered their withdrawal of service, which started Monday.

“Drivers are the real casualty of it all,” said Harry Campbell, a Los Angeles driver who runs the Rideshare Guy blog. “Basically, 10,000 drivers are barely able to earn money going forward.” (Uber and Lyft still operate outside Austin city limits, where fewer people take rides.)

Uber itself called attention to the drivers’ plight, sidestepping its own responsibility for that. “This (shutdown) is devastating to them,” spokeswoman Taylor Patterson said. “It is a huge deal for drivers’ day-to-day lives.”

On social media, Austin drivers discussed switching to a couple of much smaller ride services in the city. “I wonder if this will send a message to drivers all over the country, ‘Look, this is much more vulnerable work than you imagined?’” Dubal said. “I’m sure there are drivers who’ve bought or leased cars and rely on this for their major source of income. It’s a hugely irresponsible thing to do to them.”

Why are the companies drawing such a firm line in the sand?

For one thing, both rely on quick onboarding of new drivers, especially since both experience significant churn. Lyft even uses the same app for both drivers and riders, suggesting that riders can get behind the wheel at any point with just a few taps. Fingerprint checks slow down that process. “We don’t operate our peer-to-peer service in any market where mandatory fingerprinting requirements exist,” said Lyft’s Wilson.

Fingerprint checks can take up to four months to return results, said Dorothy Chou, Uber’s head of safety for public policy. In Houston, Uber agreed to a two-step process. After Uber’s standard vetting, drivers can work for a month, then must submit to a fingerprint check and stop driving while they wait for results. Some 19,000 drivers have opted not to continue driving. The net result: “Wait times in Houston are 35 percent higher than Austin,” she said. Lyft does not operate in Houston.

Then there’s the potential for discrimination. “We know for a fact that fingerprinting disproportionately affects minority communities,” Chou said — a position shared by social-justice nonprofits such as the Greenlining Institute.

Both companies are keen to prevent precedents. Uber and Lyft aren’t just saber-rattling, they’re broadcasting to other jurisdictions how seriously they take this issue. “Whenever a more-restrictive regulation is passed in one city, it can be a signal to others,” UCLA’s Walker said. “That’s why the soda industry fought so hard against the soda tax, for instance.”

The companies have successfully fought back legislative attempts in California to impose fingerprint background checks. Now the state Public Utilities Commission, which regulates Uber and Lyft, has said it will revisit the fingerprint-check issue within the next two months.

Could Uber and Lyft boycott their home state — including their home city of San Francisco, a critical market for both?

“Yes, it could happen here,” Dubal said. “It would be the smart thing to do, as the rest of the country looks to California on how to regulate Uber and Lyft, so they’d have a strong incentive to push back.”

But more likely, the political theater in Austin will send a message to California regulators to choose their battles carefully. “In most of these political battles, Uber, Lyft and politicians eventually work it out — and it almost always works out in Uber and Lyft’s favor,” Campbell said.

Carolyn Said is a San Francisco Chronicle staff writer. Email: csaid@sfchronicle.com Twitter: @csaid