But demonstrators who fail to inform authorities of protest plans and locations and to secure a permit are on far shakier legal ground, he added. In those cases, actions like blocking a street would most likely be subject to prosecution. Most of the proposals appear to address protests that lack permits.

In many cases, the bills’ sponsors emphasize that they are trying to improve public safety or keep order, not squelch free speech.

“We support the First Amendment altogether and want people to get out and do what they want,” said State Senator George B. Gainer, Republican of Florida, who has proposed legislation that would raise fines for blocking traffic and, like the Tennessee measure, indemnify drivers who accidentally hit protesters. “But they shouldn’t endanger themselves or others.”

Some free-speech advocates, however, have their doubts. “There are already laws on the books in states that say if you break something or harm somebody, you’re going to be prosecuted,” said Patrick F. Gillham, a sociologist at Western Washington University who studies protests. “They’re troubling. They potentially have a chilling effect on protest.”

In Georgia, where the State Senate has passed legislation toughening the penalty for obstructing traffic, Worth Bishop, a volunteer for the anti-Trump movement Indivisible, said the proliferation of protest-related bills took aim at the First Amendment.

“These laws are clearly designed to abridge the right of the people to lawful assembly,” Mr. Bishop said. He called the proposals “intimidation from the right,” saying there was scant demand for the measures from the police.