SYDNEY, Australia — When Craig Chung, an up-and-coming Sydney city councilor, meets with former officials from the United States, neither the media nor his constituents seem to care.

But for events with fellow ethnic Chinese, he errs on the side of caution. He researches the people involved. He sidesteps certain photographs and publicly declares whom he talks to and why — all to ensure he doesn’t end up accused of associating with someone tied to the Chinese Communist Party.

“There is this fear that we may work closely with somebody who is accused of being an agent of another government,” said Mr. Chung, 49, a fourth-generation Chinese-Australian. “We’re in a position now where people are running scared.”

Australia has been thrown into turmoil over allegations that China is trying to buy its politicians and sway its elections, charges that have led to increased scrutiny of the rising superpower’s efforts to influence Australia — and fears that a campaign to stamp out Chinese influence risks becoming a McCarthy-esque witch hunt.