Many of the world’s largest consumer technology companies will be closely monitoring a federal court hearing in Montana on Thursday that could decide whether TikTok will have to stop operating in the state next year.

The popular video-sharing app is suing Montana to halt a first-of-its-kind state law that would ban TikTok in the state on Jan. 1. The law was drafted by Montana’s Republican attorney general and signed by its governor in May. TikTok is asking the court to block the ban through a preliminary injunction.

Montana is at the forefront of a crusade by state Republican officials to rein in Big Tech. Republican governors, attorneys general, lawmakers and conservative policy groups say internet platforms like TikTok, Instagram and Snap are undermining conservative family values and preventing parents from protecting their children from harmful content and online predators.

Many also believe that such platforms censor conservative political views and that TikTok, whose parent company, ByteDance, is based in China, poses security risks to American users.

Republican state lawmakers have introduced several first-of-their-kind state bills that would regulate popular social media apps, like TikTok, and adult sites, like PornHub. Focusing on issues like giving parents control over their children’s online activities and stopping online content moderation, the states have significantly outpaced their Democratic counterparts in setting rules that tech companies have called aggressive and legally dubious.

Civil rights groups have warned that the new social media laws giving more control to parents could curb young people’s access to sexual health information, inhibit their ability to organize protests and cut them off from L.G.B.T.Q. communities.

Since 2021, state legislatures have passed at least 38 bills regulating social media content moderation, children’s social media use, children’s and consumers’ online privacy and online pornography, according to data from the National Conference of State Legislatures, a bipartisan policy research group; the Free Speech Coalition, a group representing the adult entertainment industry; and other organizations that track state bills.

Of these laws, states with Republican governors and Republican-controlled legislatures passed 21 — or 55 percent — of the measures. At the same time, Democratic-led states passed just 10, or 26 percent, of the laws. States with split Republican and Democratic control enacted seven laws, or about 18 percent.

At least 32 states — a majority of them led by Republicans — have also banned TikTok from government-issued devices or state networks through new laws or state orders.

On Tuesday, Utah sued TikTok, accusing the company of deceiving parents about the safety of the platform. That followed the state’s passage of a landmark law in March that would require parental consent for anyone under 18 to sign up for social media accounts and would let parents see their children’s posts and messages.

“It’s about parental rights, about making sure that parents and families can make the decisions that are best for their kids,” Gov. Spencer J. Cox of Utah, a Republican, said in an interview this week.

“I think it won’t be long until you see blue states doing exactly what we have done,” the governor added.

On Wednesday, New York lawmakers introduced a bill that would prohibit minors from using “algorithm-based social media” without permission from their parents.

Alex Haurek, a spokesman for TikTok, said that the Montana ban was “unconstitutional” and that TikTok had “industry-leading safeguards for young people,” including prompts for users under 18 to log off after 60 minutes and parental controls for teens.

Antigone Davis, Meta’s global head of safety, said the issue required “a comprehensive approach.”

“Teens move interchangeably between many websites and apps, and social media laws that hold different platforms to different standards in different states will mean teens are inconsistently protected,” she said in a statement.

Snap declined to comment.

Republican lawmakers have for years accused social media platforms like Facebook and Twitter of being biased against conservative views. But Republican state legislators steered clear of new laws regulating the companies.

That started to change in 2021 when some platforms banned former President Donald J. Trump after the Jan. 6 riot at the U.S. Capitol. That year, legislators in Florida passed the first state law making it possible to fine social media platforms that permanently banned candidates running for office in the state. Texas soon followed, passing a law allowing private citizens to sue the platforms if their posts were taken down because of their political viewpoints.

The new measures have run into roadblocks. NetChoice and the Computer and Communications Industry Association, lobbying groups that represent Google and Facebook, sued to block both laws. A federal judge in Florida temporarily stopped the state’s law from taking effect and an appeals court largely upheld that ruling. But an appeals court in Texas overruled a lower court judge who had blocked the law. The Supreme Court, which often weighs in on disputes between appeals courts, recently agreed to hear the cases.

More recently, federal judges in Arkansas, California and Texas blocked three other new tech laws, saying they likely hindered free speech rights.

A report published last year by two conservative think tanks, the Ethics and Public Policy Center and the Institute for Family Studies, was a catalyst for the laws targeting online pornography and social media, according to Republican state legislators in Utah and Louisiana. The report, “Protecting Teens From Big Tech,” provided a blueprint for states seeking to give parents more control over their children’s internet use.

The report’s recommendations included requiring age verification for pornography websites and social media platforms and requiring social media platforms, like Snapchat, TikTok and Instagram, to give parents access to accounts created by children under 18. The report also recommended that states required social media companies to block minors’ access by default to their accounts from 10:30 p.m. to 6:30 a.m.

“Tech companies do not have the right to speak to children over or against their parents’ authority,” said Clare Morell, an author of the report who is a senior policy analyst at the Ethics and Public Policy Center. “We are trying to restore parental authority and oversight.”

TikTok, in particular, is a sore point for lawmakers. A handful of Republican-led states filed lawsuits against the company and have banned the app in their states.

Montana’s ban is sweeping. If enacted, it would fine TikTok and app store operators, like Google and Apple, for violations. It attracted fierce criticism from creators of online content as well as the American Civil Liberties Union and tech trade groups.

The new law’s supporters include 18 other Republican state attorneys general, led by Jason S. Miyares of Virginia. Last month, they filed a brief asking the court to deny TikTok’s request to block the law.

They wrote that TikTok had harmed children in Montana and their states through dangerous “challenges” and noted that states had long had the power to protect their citizens from deceptive and harmful business practices.

Austin Knudsen, Montana’s attorney general, told The New York Times this summer that he believed his Republican colleagues in other states were watching the case closely to gauge how to proceed with TikTok and that he anticipated it would eventually head to the Supreme Court.

A bipartisan coalition involving more than 40 state attorneys general is investigating whether TikTok’s design and practices have caused or exacerbated mental and physical health issues among teens and children. That investigation is active. But Utah forged ahead and sued TikTok on its own this week.

“We didn’t want to wait around,” Governor Cox said. “We wanted to get going.”