One afternoon as the Shulers drove to the local library, where Mr. Shuler had been writing his blog since they could no longer pay for their Internet connection, a member of the Sheriff’s Department pulled them over, saying they had run a stop sign. The officer then served them the papers, which the Shulers refused to accept, contending that service under such a pretext was improper.

“We were both throwing the papers out of the windows as we were driving off,” Ms. Shuler said in an interview.

The Shulers missed a hearing the next day, and the restraining order was superseded by a similarly worded preliminary injunction, which some free-speech advocates saw as a clear violation of Mr. Shuler’s First Amendment rights.

“It seems to me that the judge’s order was really way out of bounds,” said David Gespass, a civil rights lawyer in Birmingham, who was further troubled by the judge’s initial decision to keep the case under seal.