Red vs. Red in Texas, With Republicans Battling One Another After Mask Order

Mr. Abbott, who faces re-election in 2022, was the first Republican governor of Texas in modern time to be officially reprimanded by a group of Republican county leaders.

“We feel that Abbott is going overboard in shutting down the economy,” said Lee Lester, the chairman of the Harrison County Republican Party in East Texas, one of the eight counties that censured the governor.

Mr. Lester, a retired insurance salesman who lives near the Louisiana border in a county that has recorded more than 500 coronavirus cases and more than 60 deaths, said Mr. Abbott needed to “start acting like we think he should act, and that is looking at the overall picture — following the facts, not fear tactics.”

The divide has been evident in and around Fort Worth, the largest conservative-led city in Texas. Republicans in urban, suburban and rural Texas disagree on how the government should respond to the virus, and on whether masks cross a line.

Mayor Betsy Price of Fort Worth, a Republican, expressed empathy rather than criticism for the governor and was as pro-mask as the Democratic mayors of Houston and other major cities. “Y’all wear a mask,” Ms. Price said in a recent public service announcement, through a white mask decorated with the silhouette of a Texas longhorn, the logo of a city whose nickname is Cowtown.

“It’s been a very measured approach in Fort Worth, not much knee-jerk reaction,” she said in an interview. “People are very much afraid, and when they’re afraid, they tend to be very critical of things.”

But nearby in the same county, in the affluent suburb of Colleyville, Mayor Richard Newton took a more aggressive approach. In April, he opened restaurants before state rules allowed it, and last month, he bucked a county mask order. “We just choose not to participate,” Mr. Newton told reporters at the time.