Spain will become the first team from outside Africa to play in Malabo since Obiang took power in 1979. Equatorial Guinea is coached by former Spain international Andoni Goikoetxea.
More than 14,000 people have joined the opposition group in calling for the match to be halted by signing a petition on change.org.
"The adequate decision for everyone, in our opinion, would be that the game is not celebrated," the group said on Thursday in a statement. "If not, Spain will pay a hefty bill for falling into this trap, and not just from an economic standpoint."
Amnesty International, EG Justice and Human Rights Watch are among those who have criticized Obiang's government over issues such as politically motivated arrests and lack of freedom of speech. Obiang, who seized power in a coup, has managed to be photographed alongside United States President Barack Obama while at the same time be accused of draining his nation's oil wealth to fabulously enrich family and cronies while his people suffer in slums.
Equatorial Guinea boasts Africa's highest per capita gross national income of nearly $18,000 a year, one of its smallest populations of about 700,000, and the most glaring disparity in the world with more than 60 percent of the population living on less than $1 per day, according to the U.N. Development Assistance Framework. It gained independence from Spain in 1968.
Spain striker Fernando Llorente was asked his opinion of the situation, but team spokeswoman Paloma Antoranz interjected and said the players would not answer questions on the topic. That set off a tense back-and-forth between Antoranz and the journalist, as the Spanish federation spokeswoman made it clear that questions about the trip had already been addressed before the journalist asked if they did not live in a "free" country where such questions could be delivered.
After Antoranz finally relented, gazes shifted to Llorente who said: "I only want to talk about sport, everything else I don't want to talk about it."
Marc Bartra, who has been called up for the first time and has yet to play for Spain, and Raul Albiol also avoided talking about the situation in detail.
"We try to stay out of all this and to focus on the football. The country, its government, that is something apart," Albiol said. "We're here to play a friendly and nothing more."
Spain defender Sergio Ramos was critical of another extended travel plan that will see the team return to South Africa for a friendly on Tuesday, its first trip to the country since it won the World Cup there in 2010.
"It's clear that these long trips are not enjoyable for anybody," Ramos said. "We can try new tactics heading into the World Cup which is always something positive."
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Follow Paul Logothetis on Twitter @PaulLogoAP
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Online: http://www.change.org/es/peticiones/que-la-selecci%C3%B3n-espa%C3%B1ola-de-f%C3%BAtbol-no-juegue-en-guinea-ecuatorial