ROME (Reuters) - Pope Francis’ hard-hitting criticisms of globalization and inequality long ago set him out as a leader unafraid of mixing theology and politics. He is now flexing the Vatican’s diplomatic muscles as well.

Last year, he helped to broker an historic accord between Cuba and the United States after half a century of hostility.

This past week, his office announced the first formal accord between the Vatican and the State of Palestine -- a treaty that gives legal weight to the Holy See’s longstanding recognition of de-facto Palestinian statehood despite clear Israeli annoyance.

The pope ruffled even more feathers in Turkey last month by referring to the massacre of up to 1.5 million Armenians in the early 20th century as a "genocide", something Ankara denies.

After the inward-looking pontificate of his scholarly predecessor, Pope Benedict, Francis has in some ways returned to the active Vatican diplomacy practiced by the globetrotting Pope John Paul II, widely credited for helping to end the Cold War.

Much of his effort has concentrated on improving relations between different faiths and protecting the embattled Middle East Christians, a clear priority for the Catholic Church.

However in an increasingly fractured geopolitical world, his diplomacy is less obviously aligned to one side in a global standoff between competing blocs than that of John Paul’s 27-year-long papacy.

This is reinforced by his status as the world’s first pope from Latin America, a region whose turbulent history, widespread poverty and love-hate relationship with the United States has given him an entirely different political grounding from any of his European predecessors.

"Under this pope, the Vatican’s foreign policy looks South," said Massimo Franco, a prominent Italian political commentator and author of several books on the Vatican.

He said the pope has been careful to avoid taking sides on issues like Ukraine, where he has never defined Russia as an aggressor, but has always referred to the conflict between the government and Moscow-backed rebels as a civil war.

That approach is intended to ensure he remains more credible with countries like Syria, Russia or Cuba, all nations where Francis feels he can help local Christians best by steering an independent course.

DIPLOMATIC RISKS

Francis already has his hands full overhauling the Vatican’s complex internal bureaucracy after a series of financial and sexual scandals involving abuse of children by priests which date back decades.

But clearly deeply interested in how the world outside the walls of the Vatican works, he appears determined to use his position and the huge global audience he commands to challenge entrenched diplomatic positions as well.

The former secretary of state, Cardinal Tarcisio Bertone, a veteran insider whose office formerly controlled both relations with foreign powers and many internal Vatican affairs, has been replaced. His office has been downgraded to resemble a more classical diplomatic service while Francis has set a bolder, more personal stamp on Vatican foreign policy.

"He’s someone who’s capable of praying in the Blue Mosque in Istanbul and then talking about the Armenian genocide. He’s not someone who’s bound by political correctness," said former Italian Foreign Minister Franco Frattini.

"It’s the diplomacy of a real leader."

Whether it is to the taste of all the world’s 1.2 billion Catholics, world politicians with priorities of their own or even the many layers of the Church’s own administration is another matter.

With many conservative Catholics unhappy about the pope’s focus on issues like economic injustice and his relatively tolerant tone on sensitive social topics like homosexuality and the status of divorced people, pronounced views on delicate diplomatic issues could cause further division in the Church.

It is a point where he will be particularly tested in September on his upcoming visit to the United States, where some conservative U.S. Catholics are openly hostile.

After helping to foster last year’s agreement reviving diplomatic relations between Havana and Washington, Francis reaped criticism from many U.S. conservatives, including Marco Rubio, a candidate for the Republican nomination for president.

Rubio, the son of Cuban immigrants and a practicing Catholic, avoided directly admonishing the pope, but said he should "take up the cause of freedom and democracy" in Cuba.

That kind of veiled criticism from a politician who would normally be considered a staunch Church ally reflects the wider unease some Catholics feel at the change Francis has ushered in at one of the world’s most conservative institutions.

"Bishops complain that he becomes popular by attacking the Church," said Franco.

"He speaks directly to the people and doesn’t respect the usual command structures. He decides on his own or with people who are not those who previously had a central role."

(Editing by Crispian Balmer)