State Representative Ramon Romero Jr., a Democrat who in 2014 became the first Latino elected to the Texas Legislature from Fort Worth’s majority-white Tarrant County, said the anti-immigrant rhetoric in the state has been too divisive for too long.

“I think if the shooter’s manifesto would not have come out, it wouldn’t have been so glaringly obvious,” Mr. Romero said. “I’ve said for a long time that I felt this was a dangerous conversation that was going to eventually rear its ugly head. Any criticism that the governor has received has been absolutely warranted, and he should be the first one to say, ‘I made a mistake.’”

A spokesman for Mr. Abbott declined to comment.

If there was any Republican criticism of the governor’s mailer, it was muted. Some Republicans expressed outrage that Democrats were branding the letter as racist. They said the letter was not anti-immigrant but anti-illegal immigration, and that it was wrong for the Texas Democratic Party to imply that opposing illegal immigration was racist.

Matt Mackowiak, a Republican consultant who is the chairman of the Travis County Republican Party in Austin, said he found nothing offensive about the governor’s letter. “Texas has invested billions of dollars and deployed thousands of personnel to the southern border to do a job that the federal government’s not willing to do,” Mr. Mackiowiak said. “I read the mailer. I didn’t see anything in there that was objectionable.”

The El Paso gunman echoed talking points used in the past both by Mr. Trump and by Texas Republicans who have called for stronger measures against illegal immigration.

The lieutenant governor, Dan Patrick, was quoted in The Texas Observer in 2006, when he was running for a State Senate seat, describing undocumented immigrants as invaders and saying that the main “problem we are facing is the silent invasion of the border. We are being overrun. It is imperiling our safety.”