Men are viewed as the heads of the household and the church by one of Australia's largest Christian bodies.
But that might be labelled gender-based violence and censored under a looming online safety overhaul, they claim.
Religious leaders will join broadcasters, gambling reformers and think tanks, as well as the national online safety watchdog, in Senate hearings examining Labor's proposed digital duty of care on Tuesday.
The law would force social media to protect children from content promoting crime or eating disorders, as well as pornography, misogynistic content and posts that cause distress.
Sydney's Anglican Diocese is pleading for more specificity over concerns the bill's hefty fines for tech giants will encourage "over-censorship", including of its teachings.
"Biblical teaching on male headship in marriage and in the church, and the ordination practices of some churches, are characterised by some critics as promoting 'control' or as a form of abuse," Bishop Michael Stead wrote in a submission to the Senate inquiry.
Women cannot be ordained as priests in the Sydney diocese despite many Anglican bodies allowing it, including its Melbourne counterpart.
"There is a real risk that automated moderation systems would classify such teaching as promoting gender-based non-physical violence," the submission continues, adding the church's stance on transgenderism might also fall foul of the new laws.
"If the regulator characterises ... the Biblical teaching that humanity is created male and female as gendered violence, then sermons, Bible studies and online comment expressing that teaching may well be treated by providers as promoting gender-based violence."
The sentiment was echoed by the Australian Catholic Bishops Conference, that wrote "longstanding religious teachings on matters of ... human relationships" could be unwittingly captured.
"Legislation directed at addressing genuinely harmful conduct should not create incentives for the suppression of religious, moral or political viewpoints just because they might be contested," it said.
The organisation suggested a religious carve-out from the duty of care bill, which already exempts professional news, educational and public interest content.
The Australian Jewish Association in its submission argued fines of up to $109.2 million for platforms that don't comply meant they would err on the side of censorship.
It added the bill was scant on what happens when companies incorrectly removed lawful content or restricted accounts.
The coalition has already turned against the digital duty of care over the alleged censorship risk, which has been rejected by Labor.
On Tuesday, the federal eSafety commissioner is also expected to call for tougher enforcement on artificial intelligence-powered "nudify" apps, which have been used to undress people in photos, including children.
Users can sidestep existing restrictions on these sites by copying down their web links, even if the apps don't appear in search results.
"Market intelligence shows that many Australian users access nudify websites directly from the URL or via referral websites," the watchdog wrote in its submission.
It will ask for the power to direct telecommunications companies to cut the apps off entirely.
Lifeline 13 11 14
Fullstop Australia 1800 385 578
