Jacob Monty is not a RINO — a Republican in Name Only — even though some of his hate mail says otherwise. Mr. Monty, an immigration lawyer in Houston, has been deeply involved in Republican politics in Texas and nationally for much of the past 20 years. He was a fund-raiser for both of George W. Bush’s campaigns, and estimates that he has personally contributed more than $250,000 to Republican candidates.

But this year’s presidential race has pushed Mr. Monty to abandon his party’s presidential nominee.

On Aug. 20, Mr. Monty and a group of Hispanic Republicans on an advisory council to Donald J. Trump gathered at Trump Tower in New York to discuss Mr. Trump’s immigration proposals. They left with the impression that Mr. Trump had changed course and would put forward a plan that included a path to legal status for some undocumented immigrants. Mr. Monty said he felt that he’d just met “the real Donald Trump.”

“I connected with him — I think everyone at the table did,” he said. He added: “I’m not going to say who I think the real Donald Trump is. I think I met him on Aug. 20.”

Whomever he met then, someone else spoke at the end of the month, when Mr. Trump used a speech in Phoenix to double down on his hard-line position on immigration, call for a “new special deportation task force” and lay the blame for all of society’s ills — from crime, to joblessness, to an implicit loss of America’s cultural identity — squarely at the feet of immigrants.