WASHINGTON — Thomas Lambert, a professor at the University of Missouri’s law school, gave his former colleague Josh Hawley a warning before Mr. Hawley became a senator in January.

Mr. Lambert had been wary of Mr. Hawley’s decision in 2017, as Missouri’s attorney general, to open an antitrust investigation into Google, saying he didn’t see the state’s logic for the case. While he wished Mr. Hawley well in Congress, and said he was glad they were friends, Mr. Lambert also noted that he would continue to speak out when he disagreed with the senator’s policy positions.

“And he said, ‘I assume you mean on things like tech,’” Mr. Lambert recalled recently. “And I said, ‘Well, mainly.’”

Their interaction highlights a deepening divide in Washington and around the country. The rising movement in the United States to consider charging the country’s biggest tech companies with violating antitrust laws is running headlong into powerful and well-funded conservatives and libertarians committed to pushing back on those efforts. They include academics like Mr. Lambert; lawmakers like Senator Mike Lee, Republican of Utah; and groups like the Koch political network and others that are connected to the tech companies themselves.