The source said this is a "full stop" on Unanue speaking to the press, not only about politics, but also about the company itself.
A majority of Goya shareholders favor removing Unanue altogether but have been prevented from doing so by the dynamics of the family-controlled company, according to the source.
"The company has never been political or politicized," said the source. "He's gone from bad CEO to CEO that has imperiled the future of the company and endangered the lives of some of the shareholders," the source said in reference to some Unanue family members having allegedly received threats because of the CEO's comments.
"His statements are insulting and dangerous," said the source.
Unanue spoke to the New York Post after the board's action but did not directly discuss his censure or the ban on speaking to the media. He confirmed he would no longer be speaking publicly about politics or religion.
"Independently, I've made the decision to lower the temperature and walk away from speaking about politics and religion," he told the Post. "I realize it's important because of the diverse views of the company and our market."
A history of controversy
On inauguration day, shortly after President Trump made his farewell remarks, Unanue appeared on Fox Business' morning show and told anchor Maria Bartiromo that there was a "war coming" and that President Joe Biden's election was "unverified."
"They accomplished what they set out to do, which was get President Trump out of the way," he said. "I think this is mission accomplished, by the unions, the partnership, the conglomerate of social media, big tech, big media and big government. ... There is a war coming, now that the president is leaving today, they're still coming after the United States, the working class."
Unanue set off the controversy in July when, appearing at a White House event, he said, "We are all truly blessed ... to have a leader like President Trump who is a builder. We have an incredible builder, and we pray. We pray for our leadership, our president."
Unanue and Goya said at the time that he was at the White House to announce the donation of millions of cans of Goya products to food banks.
"It's hard to really say [the controversy hurt sales] but sales growth is less than it was pre-him speaking at the Rose Garden," said the source.
Goya did not respond to requests for comment from CNN. The company, founded in 1936 by Don Prudencio Unanue and his wife, Carolina, now has more than 4,000 employees in 26 facilities throughout the United States, Puerto Rico, the Dominican Republic and Spain, according to the company's web site.