Trump's rise has put evangelical Latinos like Rodriguez in a difficult position. Many view the Democratic Party as hostile to conservative Christian values. Many also say they cannot support Trump, who has alienated Latinos by insulting Mexican immigrants as drug dealers and rapists and pledging to build a massive border wall.
"We have a problem with the donkey, and we have a problem with the elephant," Rodriguez said at his group's annual convention in Anaheim last weekend, where Trump and Hillary Clinton, the likely Democratic nominee, both addressed the crowd in videotaped remarks.
It's a problem of great significance, given the size of the Latino vote and the growing influence of evangelicals in Latino communities.
A record 27 million Latinos will be eligible to participate in the November general election, a figure that includes a rising number of evangelical Christians.
While a majority of Latino adults still belong to the Catholic Church, more and more are embracing evangelical Christianity, according to Pew Research Center. The percentage of Latinos who identify as evangelical or born-again Christian rose from 12 percent in 2010 to 16 percent in 2013, according to Pew.
Evangelical Latinos, who tend to hold more conservative social views than their Catholic and non-religious counterparts, have long been viewed as potential recruits for the GOP. According to Pew, they are more likely to identify as Republicans than are other Latinos.
But Trump's attacks on the immigrant community have forced some Latino evangelicals to put identity politics ahead of their religious beliefs.
"In good consciousness, I just can't vote for him," said Eddie Rodriguez, a pastor who leads an Assemblies of God congregation in South Florida.
Not only does he think Trump has set back the U.S. in terms of racial relations, he doesn't believe Trump is a true Christian conservative. He cites Trump' past support for abortion, his harsh tone toward women and his acknowledgement that he has never asked God for forgiveness.
Rodriguez supported Rubio in the Republican primaries, but has now resigned himself to voting for Clinton.
"It's extremely difficult," he said. "I have to pick between two people I disagree with."
That's a dilemma faced by the broader evangelical community, which has been divided between those who support Trump and those who have denounced his language and ideas as un-Christian.
Next month, several hundred conservative leaders plan to meet privately with Trump to address concerns about his candidacy. The meeting, which was arranged by former presidential candidate Ben Carson, is expected to include some Latino leaders.
Some of those evangelical Latino leaders are winnable for Trump.
Sergio De La Mora, who helps lead a Latino megachurch in San Diego, said he admires Trump's business experience and doesn't feel personally offended by his rhetoric on immigration.
That might be because he and his congregants have long ties to the U.S. and little connection to illegal immigration, he said.
"Most people really don't care about that," said De La Mora, who said he is considering voting for Trump.
Still, when it comes to Latinos, Trump is operating at a major deficit.
According to a recent Fox News Latino poll, 62 percent of Latinos supported Clinton, while only 23 percent backed Trump.
That would give the real estate mogul and former reality television star even less Latino support than Mitt Romney, who won just 27 percent of the Latino vote as the Republican nominee against President Barack Obama in 2012. Romney's bid suffered in part from his proposal to make life difficult for immigrants in the country illegally so that they self-deport.
After Romney's loss to Obama, the Republican National Committee issued a report that said future Republican survival would require candidates to soften their rhetoric on immigration and the Latino community.
"If Hispanic Americans perceive that a GOP nominee or candidate does not want them in the United States ... they will not pay attention to our next sentence," the report said. "It does not matter what we say about education, jobs or the economy, if Hispanics think we do not want them here, they will close their ears to our policies."
Former Republican presidential candidates Bush and Rubio both campaigned based on that playbook, promising to pass legislation that would allow immigrants in the country illegally to stay with some form of legal status. While those proposals won them fans among Latino conservatives, they were not enough to stop Trump.
Since becoming the presumptive nominee this month, Trump has toned down his rhetoric slightly and has made a few overt pitches to Latino voters. On Cinco de Mayo, he tweeted a picture of himself with a taco salad and wrote: "I love Hispanics!"
But some Latino evangelical leaders say it will take much more than that for them to consider voting for him.
"We're people of faith, so our response is: 'Say you're sorry. Repent. Make it right,'" said Tony Suarez, an evangelical pastor from Virginia who was in Anaheim for the conference. "The ball is in his court," he said.
In his videotaped remarks to church leaders last Friday, Trump did not apologize. Instead he told them he would win the election in November and that they were "going to like President Trump."
"I'm going to win, and we're going to take care of everybody," Trump said, vowing to help poor and middle-class minority communities by lowering taxes, improving schools and creating jobs. "We're going to take care of you."
Trump abstained from the heated rhetoric on immigration. Clinton, in her taped remarks, wasn't about to let the audience forget exactly what Trump has said.
"We're hearing some divisive and dangerous rhetoric in this election," Clinton said. "We have a candidate who wants to tear families apart and forcibly deport 11 million undocumented immigrants -- who calls Mexicans rapists."
The Rev. Walter Contreras, a pastor in Pasadena who skipped the event, said simply giving Trump a platform to speak was dangerous.
Some evangelical leaders appear eager to forgive Trump because they can't stomach supporting Democrats, he said. He and other Christian leaders who share his views have led a campaign to counter that, recently writing a letter in which they said supporting Trump is the same thing as supporting his anti-immigrant message.
"We're not going to tolerate that kind of rhetoric," Contreras said. "It's very destructive. It's very real. It's too late."