The US Government's ethics code bans those in public office from endorsing products, and the Trumps' posts have prompted a barrage of criticism for blatantly violating the rules.
The posts appeared after Robert Unanue, CEO of Goya Foods, the largest Hispanic-owned US food company and a popular brand among Latino Americans, appeared with Mr Trump on Thursday for the signing of an executive order creating an advisory panel aimed at spurring Hispanic prosperity.
Mr Unanue was full of praise for the president.
"We're all truly blessed at the same time to have a leader like President Trump who is a builder, and that's what my grandfather did," said Mr Unanue, the third generation of his family to run the business. "We pray for our leadership, our president, and we pray for our country that we will continue to prosper and to grow."
But many Goya consumers were not impressed and the company fast became the target of a boycott campaign on social media, with the hashtags #Goyaway and #BoycottGoya trending on Twitter.
The event at the White House came as Mr Trump's re-election campaign sought to boost his standing among Hispanics, who have often felt alienated by his policies and political rhetoric.
Reuters/Ipsos national polling shows only about a quarter of registered Hispanic voters chose Mr Trump in a match-up with his Democratic rival, former vice president Joe Biden.
Among those in the forefront of calls for a boycott were two leading Hispanic politicians in the Democratic Party - former presidential candidate Julian Castro and US Representative Alexandria Ocasio-Cortez of New York.
Mr Castro tweeted that Goya had been a staple of many Latino households for generations.
"Now their CEO, Bob Unanue, is praising a president who villainises and maliciously attacks Latinos for political gain," he said. "Americans should think twice before buying their produces."
Ms Ocasio-Cortez suggested to her 7.5 million followers on Twitter that they find homemade alternatives to Goya's popular Adobo seasoning.
United We Dream, an immigrant youth-led social action group, launched an online boycott petition that said Mr Unanue had "aligned the Goya brand with Trump's white supremacist agenda".
"If Goya wants our business, they must respect and fight for our humanity," the group said.
Mr Unanue defended his comments, however, and said on Friday that the calls for a boycott of the company amounted to an attack on his freedom of speech.
"I'm not apologising," he told Fox News. "When you're called by the president of the United States, you're going to say, 'No, I'm sorry, I'm busy, no thank you?' I didn't say that to the Obamas and I didn't say that to President Trump."
Separately on Fox News, White House adviser Kellyanne Conway decried the controversy. "It's just a shame that people make everything so politicised, including food," she said.
Countering online calls for a boycott was the emergence of the #BuyGoya hashtag. Hollywood actor James Woods praised Mr Unanue for setting "a good example in the fight against liberal terrorism."
US Senator Ted Cruz said on Twitter that his grandparents ate Goya black beans twice a day for nearly 90 years. "And now the Left is trying to cancel Hispanic culture and silence free speech," the Texas Republican said.
Politically motivated calls for economic boycotts have become commonplace on social media in recent years, with mixed results.
It was too soon to tell whether the anti-Goya campaign would generate enough support to damage the bottom line of a privately owned company that ranks among the leading distributors of packaged Latino foods in the United States, Europe and the Caribbean.
Additional reporting by AFP.