“Plaintiffs keep taking cracks at it, and every time they don’t instantly lose, they pour more resources into that crack to see if they can split it open,” said Eric Goldman, a Santa Clara University law professor who supports the law.

Ms. McAdams’s case is one of the widest cracks today. Facebook asked Steven Kirkland, a state judge in Houston, to dismiss two of Ms. McAdams’s lawsuits because of its immunity under Section 230. The judge denied the company’s motions, though his rulings offered little insight into his thinking. He declined to elaborate in an interview.

“It’s always noteworthy when a 230 dismissal isn’t granted in a case involving someone like Facebook, because we just presume Facebook won’t be liable for what its users are doing,” Mr. Goldman said.

Facebook responded to the judge’s decision in Houston with a nearly 50-page petition to a Texas appeals court, arguing that Judge Kirkland had erred. “The claims here asserted against Facebook have no basis in law,” Facebook’s lawyers wrote in the petition.

A Facebook spokeswoman added that the company “has zero tolerance for any behavior or content that exploits children on our platform” and that it used sophisticated technology and a partnership with a children’s advocacy group “to aggressively combat this behavior and protect children.”

Ms. McAdams’s approach could prove significant. If the Texas rulings hold up on appeal, they could persuade judges in other states and potentially even draw the Supreme Court to weigh in, said Jeff Kosseff, a United States Naval Academy law professor who wrote a book on Section 230.

If judges began allowing such product-liability claims to get around Section 230, it would probably mean many more companies would be held legally responsible for harms that occurred on their sites, particularly if plaintiffs could show the companies’ decisions or policies had led to those harms, according to Mr. Kosseff and two other law professors who spoke to The New York Times.