SEOUL (Reuters) - For the first time in years there are liberal presidents in South Korea and the United States, but the change in U.S. administrations hasn’t made it any easier for Seoul to balance its alliance with Washington and its economic reliance on China. China has dominated the agenda of an Asia tour by U.S. Secretary of State Antony Blinken and Defense Secretary Lloyd Austin, who arrive in South Korea on Wednesday for talks, casting its shadow even over core issues like the North Korea nuclear threat and strengthening the alliance. The Americans’ message has focused on marshalling their Asian alliances to counter potential “coercion and aggression” by Beijing. That represents a challenge for Seoul, which is not eager to provoke China - its largest economic partner. President Moon Jae-in also needs the backing of both U.S. President Joe Biden and the Chinese to have any hope of achieving a breakthrough with Pyongyang in his final year in office. There’s a paradox where the liberal governments in Seoul and Washington agree on issues like climate change, public health, and equality, but have disagreements over bilateral relationships with places like China, North Korea, and even U.S.-allied Japan, said John Delury, a China expert at South Korea’s Yonsei University. “When you frame the U.S.-South Korea relationship in terms of those countries then there is a lot of disagreement and it’s hard to find common ground,” Delury said. “So the emphasis on those issues in some of the messaging is not really finding common ground, but rather highlighting differences.” ‘NATIONAL INTERESTS’ South Korea paid a steep economic price after it angered China in 2017 by deploying a U.S. Terminal High Altitude Area Defence (THAAD) anti-missile system that features radar which Beijing believes could be used to penetrate its territory. The economic fallout cost South Korea $7.5 billion in lost income in 2017 alone, according to estimates by the Hyundai Research Institute, while the Bank of Korea estimated that it knocked 0.4 percentage points off South Korea’s economic growth that year. South Korea has been hesitant to frame its longstanding alliance with the United States as anti-China, and Moon’s administration has expressed scepticism toward talk of officially joining with the United States, Australia, Japan and India - a gathering dubbed the “Quad”. A senior foreign ministry official said Seoul was open to working with the Quad as long as it was based on “openness, transparency and inclusiveness”. “We will have in-depth discussions with the United States based on those principles and make a decision according to our national interests,” the official said. The Moon government made it publicly clear it will not participate in an initiative that “excludes or contains a particular country,” meaning China, said Duyeon Kim, with the U.S.-based Center for a New American Security. “Unless the allies get very creative with nuances, it will be difficult to impossible to get this particular progressive South Korean government to join such democratic coalitions,” she said. Some South Korean officials think South Korea may have no choice but to sign on with Washington’s campaign against China, and that it could serve Seoul’s interests in the end, including on North Korea, said one diplomatic source familiar with their thinking. “The Quad is indeed an effort to build a bulwark against China, and joining it would give Seoul more leverage in both driving Washington to restart talks with the North Koreans, and dealing with Beijing, though it would risk causing some discomfort in China relations as an immediate impact,” the source said. South Korea’s desire to avoid antagonising China while strengthening ties with the United States may be a useful reality check for American officials, Delury said. “South Korea’s desire to get along with both the U.S. and China is shared pretty widely across the region,” he said. “I’m not sure it’s sustainable to push on a hawkish Indo-Pacific when that’s not what the Indo-Pacific wants.”