He then taught chemistry, physics, and music at Salesian colleges in El Salvador, Honduras, and Guatemala over the next fifteen years.

[3] Rodríguez was created Cardinal-Priest of Santa Maria della Speranza by Pope John Paul II in the consistory of 21 February 2001.

"[11] Reflecting on the reorganisation of the Roman Curia, his advisory role to the pope and Catholic response to climate change.

The cardinal made the comment in a 23 September interview with Catholic News Service in New York, where he was participating in interreligious meetings in his capacity as president of Caritas Internationalis.

Reformation of the Roman Curia, the church's central administrative offices, is a normal response to changing times, has a significant 20th-century precedent, and was a focus of the pre-conclave meetings before Pope Francis was elected, Cardinal Rodriguez said.

[12] On 10 March 2015, Rodriguez received the University of Dayton's Archbishop Oscar Romero Human Rights Award for his humanitarian work.

[17] In a May 2002 interview, Rodríguez said "It gave me considerable food for thought that, at a time of total media focus on developments in the Middle East with all the injustices being perpetrated against the Palestinian people, U.S. television and press people were obsessed with sex scandals of 30 or 40 years ago."

[18] Rodríguez believes the Church must be "open" and in "constant dialogue", following the Second Vatican Council's example in rejecting attitudes of "arrogance and superiority".

When challenged in an international interview about being unqualified for such a task, he responded quietly that he was educated in chemical engineering in Texas and knew a thing or two about petroleum.

His choice as leader, however, was not his technical knowledge but the national respect for his integrity and his neutrality towards political groups in the country.

In 2008, Rodríguez criticized President Manuel Zelaya for using public money to promote his plans instead of spending it on the poor.

[24] The Italian magazine L'espresso reported that Pope Francis assigned retired Argentine Bishop Jorge Casaretto to undertake an investigation of Rodríguez' financial management in 2017 and that his report suggested that Rodríguez may have been involved in mismanaging Church funds, and may also have accepted hundreds of thousands of dollars from the Catholic University of Tegucigalpa.

[25][26] In a 2018 book, Martha Alegría Reichmann De Valladeres, widow of former Honduran ambassador to the Holy See Alejandro Valladares Lanza, accused Rodríguez of maintaining an abusive and mafia-like regime in Honduras for decades, promoting false investment schemes, diverting money from the local university and from the government to shadowy and immoral purposes.