A Christian leader in a Muslim land: Indonesia's battle to balance religion in politics - CNBC

Adding to the explosive situation is a theory that Islam isn't actually at the heart of the political unrest.

"Rumors are circulating in Jakarta that former president Susilo Bambang Yudhoyono is actually the source of funding behind these protests," said Afrianty. That line of thinking had led moderate Indonesians to believe the protests had more to do with politics than Islam, she continued.

The rumor emerged last month after President Joko Widodo, or Jokowi, said "political actors" were exploiting the situation. Yudhoyono's family has vehemently denied involvement in the protests.

Regardless of the motive, the protests and influence of fundamentalist groups could hurt Jokowi's administration.

"This makes the job of Jokowi and other reformers, such as Ahok, much harder. For Islamists, Jokowi is seen as a secular nationalist leader who doesn't represent their Islamic identity so they want to vote him out," Afrianty said.

Before Friday's protest in Jakarta, Indonesian police said they had foiled a plot to use the protests to lead an uprising against Jokowi, Reuters reported. Police detained 10 people in the early hours of Friday, including politician Rachmawati Sukarnoputri, who is the sister of former president Megawati Sukarnoputri, as well as musician Ahmad Dhani and retired army general Kivlan Zen, Reuters said.

"The on-going political tension between religion and politics is distracting Jokowi from his main priorities, which is improving infrastructure and regulatory burden on investors," Ramage stated.

The situation could hit the economy, too, at a time when investors have praised Indonesia as a standout opportunity among emerging markets.

"Indonesia is one of numerous competitive emerging markets competing for limited investment dollars, so this becomes one more thing that investors put in the negative column if they believe political stability is under threat," Ramage warned.

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