Mr. Castro said, in an interview last month, that he senses a great deal of anxiety remaining after that attack. “There’s an urgency we need to respond with,” he said. “We have a president attacking Latinos and immigrants. There’s a real sense of going back, so of course I need to address that.”

But in a community as diverse as Latinos in the United States, there is not universal agreement. A small but vocal minority of Hispanics are steadfast supporters of Mr. Trump and dismiss any suggestion that he has encouraged racist attacks with his rhetoric.

Recent polls of Latino voters show, however, that the overwhelming majority believe they are facing increasing threats and view racism as a pressing issue. A Univision poll showed that 87 percent of Latinos who are registered to vote view racism as a significant issue, the highest percentage in nearly a decade, and some 66 percent of voters surveyed said they were “very worried” there would be another mass shooting “targeting people based on race or country of origin.”

Ms. Castro, now 72, once urged a reporter not to confuse her sons’ politics with hers — she was more radical. But during the September debate, she was pleased by Mr. Castro’s aggressiveness, and hopes it is a tone that he sticks with, especially in the debate next week.

She grew up at a time when Mexican-Americans were banned from living in certain neighborhoods in her native San Antonio, and restaurants hung signs that read “No dogs or Mexicans.” Drawing lessons from the civil rights movement, Chicano activists in the 1960s and ’70s staged protests and walkouts throughout the Southwest, demanding access to better housing, education and political power.

“During my own time and the time of the ’60s, for me much of what I did came out of anger — it was just a raw deal for our people,” she said in an interview. “I think that with my sons, there is no need to come out of anger. They come out of an educated place, an experienced place — not to say that they can’t get angry, but they’re coming out of an understanding how public policy is made and in a strategic way.”