Aaron Bianco, a staffer at St. John the Evangelist in San Diego, said a right-wing campaign against him made him fear for his family.
The victory of independent Kerryn Phelps means the Liberal Party will no longer hold a majority in Parliament.
The piece in question from LifeSite News claimed to analyze health data, but it demonized gay and bisexual men.
Ellen DeGeneres discussed the threats in a new interview with Adweek, which honored her with its Media Visionary Award.
In what seems a throwback to the 1950s, at least 19 men have been arrested this year for engaging in consensual sex at Florida's Pleasure Emporium.
A rash of anti-LGBTQ lawsuits has coincided with his confirmation, and the Supreme Court has already been asked to consider several other cases.
Antigay graffiti painted on an office wall over the weekend was just the latest incident of harassment against Aaron Bianco.