The debate over how to characterize the bomber’s nearly three-week campaign of violence has been a reminder, for many, of the ways in which race, geography and class continue to play out in a city that prides itself on tolerance and diversity.

Though Austin is widely seen as a liberal island in a deeply conservative state, the attacks have stoked the raw racial, economic, political and geographical divisions that continue to shape life here, 90 years after the city was segregated by decree. Austin and its suburbs remain sharply divided by class, race and even religion. Like Houston, it is an urban, diverse and Democratic hub surrounded by largely white, Republican suburbs, including Pflugerville, Mr. Conditt’s hometown.

“Austin has gradually started to become aware and conversant about its race issues over the past five years, so the initial suggestion that these bombings could be race-related made people deeply nervous that the problem could be that bad,” said Cecilia Ballí, a writer and cultural anthropologist who lived in Austin from 2008 to 2014 and who now lives in Houston. “Whether or not the bomber’s motive ends up being race, this brought to the forefront one of the city’s challenges and worst fears.”

The police have said that Mr. Conditt, who is white, gave no indication in a 25-minute confession left on his phone that he was driven by racial hatred. News emerged Thursday that one of the explosive packages he sent at a FedEx store was addressed to a spa employee who is white. His past statements, including the views he expressed on a community college blog opposed to gay marriage, have added to speculation that he was anti-gay.

In East Austin on Thursday, Daniel Arriaga, 51, a furniture mover, said he still believed the bomber had a hatred for blacks and Hispanics. He had harmed the two white victims, Mr. Arriaga theorized, “just to throw it off.”