By David Dolan and Elaine Lies

TOKYO, Sept 27 (Reuters) - Two months after he was assassinated, Shinzo Abe is still stirring controversy, evidence of how the polarising former premier's legacy is shaping Japanese politics on everything from defence to monetary policy.

Japan's longest-serving prime minister was a divisive figure who was dogged by scandals. The latest, involving revelations about his ruling Liberal Democratic Party's (LDP) ties to the Unification Church, an organisation critics call a cult, has caused an outcry over his state funeral and sent Prime Minister Fumio Kishida's approval rating to a record low.

Yet Kishida is expected to continue with several of Abe's policies, at least for now. That's a reflection of how Abe transformed both the LDP and Japan's policy landscape, experts say.

An unapologetic nationalist, Abe pushed the country toward a muscular defence posture that many now see as prescient amid growing concern about China, although he failed in his long-stated mission to change the pacifist constitution.

Abe's attempt to use massive monetary and fiscal stimulus to kick-start domestic demand also fell short, but Kishida has so far given little indication he might suddenly change those policies.

The current premier has also signalled he will stay the course on two of Abe's less controversial successes: the strengthening of corporate governance and using tourism as a growth pillar.

"I don't think we're seeing a reversion to something that came before" Abe, said Tobias Harris, a senior fellow at the Center for American Progress and the author of an Abe biography.

"If we look at the arc of his entire political career, the movement that he basically became the leader of in some ways succeeded. The way Japan is governed in 2022 is very different," from when Abe was first elected to parliament in 1993.

What remains less certain, however, is who will replace Abe as the leader of the party's large and powerful right wing. Until his death, Abe led the biggest faction, cementing his post-prime minister role as a behind-the-scenes king-maker.

Fear of alienating party hawks may have prompted Kishida, part of the LDP's more liberal wing, to push ahead with the state funeral, said Tomoaki Iwai, a professor emeritus at Nihon University and an expert on Japanese politics.

"So much has emerged about ties to the Unification Church since the assassination, and it's clear Abe was part of this problem," Iwai said. "I think this will prove a big miscalculation."

DEFENCE SPENDING

The LDP has promised to double defence spending to 2% of gross domestic product over five years. That would make Japan the world's third-largest military spender behind the United States and China.

Abe, whom some voters saw as too hawkish, could never deliver that kind of increase, although his government passed legislation to allow the military to fight overseas for the first time since World War Two, and reinterpreted the war-renouncing constitution to allow Japan to acquire longer-range missiles.

Many Japanese remain wary of entanglement in U.S.-led wars, although that has been tempered by alarm about Chinese military activity around Taiwan.

Kishida has "broadly been seen as more moderate, personable and overall more trustworthy by the electorate than Abe was, which gives him greater leeway in advancing the defence agenda," said James Brady, Japan analysis lead at consultancy Teneo.

Kishida has promised to increase defence spending "substantially" but has yet to give details. Brady reckons he will stop short of doubling it, and fund the increase via taxes rather than a bond issuance, which was Abe's plan.

BOJ IN FOCUS

Bank of Japan Governor Haruhiko Kuroda, an Abe appointee, has come under criticism for sticking to massive monetary stimulus and ultra-low interest rates, even as other central banks around the world have increased their rates to shore up currencies in the face of a soaring dollar.

The government intervened in the currency market last week, buying yen for the first time since 1998. Kuroda's term ends in April and his dovish deputy, Masayoshi Amamiya, is seen as the most likely candidate to replace him.

That could mean more of the ultra-loose policy and fiscal stimulus set in motion under "Abenomics".

"No one seems to have an alternative to the monetary policy mix that we have," said Harris of the Center for American Progress, adding that the LDP wasn't invested in reducing deficits. "Abe kind of won the debate, even if the results have been disappointing in may ways."

(Reporting by David Dolan and Elaine Lies; Editing by Gerry Doyle)