Liberal Party moderates have set red lines for Sussan Ley as the Coalition prepares a new immigration policy, making clear they will not abide a Pauline Hanson-lite, anti-migrant agenda, as the opposition leader ups her criticism of the One Nation leader’s burqa stunt.

Hanson grabbed the spotlight this week through her anti-Islam antics, her luring of Barnaby Joyce from the Nationals, and attempts to wedge the Coalition on a series of motions and private bills that provoked a war of words between right-wing Liberals and Nationals, and Liberal moderates.

“It was offensive. I do not want to see anyone’s religion mocked,” Ley told this masthead’s Inside Politics podcast, as she fends off a surging One Nation.

“I really take affront, offence to the forum in which it was done. There are many forums to have a view. The democracy that we share is about the contest of ideas, sure, but not on, not in the Senate. Australians expect better of us.”

In closed-door meetings, ideologically opposed Coalition MPs had heated rows over the terms “mass migration” and whether to condemn the recent March for Australia rallies. South Australian senator Andrew McLachlan, who repeatedly crossed the floor against his party this week, became irate at the prospect of adopting language on “mass migration”, while Nationals leader Bridget McKenzie insisted the Coalition could not pit itself against the March for Australia movement.

The moderates – still fuming over losing the net zero argument and displaying newfound aggression towards the right – eventually prevailed in ensuring the Coalition did not follow Hanson.

With the Senate feuding bringing to light the centre-right’s fracturing over migration, Ley has desperately tried to take hold of the debate that fuelled the frontbench departures of Andrew Hastie and Jacinta Nampijinpa Price.

Moderate MPs have made clear to Ley and her office that they will not publicly support a migration policy that puts too much emphasis on migrants being the cause of societal problems such as housing affordability, according to senior party sources unwilling to speak publicly, raising the prospect of frontbench resignations. The threat of moderates resigning over energy policy did not eventuate, but that loss was seen as the final straw for a new generation of moderates fed up with being dragged to the right and sceptical about Ley’s ability to reshape the party.

On Friday night, Hastie sent out a subscriber email flagging immigration as the next big fight for the Coalition if they want to be competitive.

“Immigration is out of control,” he wrote. “It’s bidding up housing prices and rents, and destroying our fragile social cohesion.”

Housing spokesman and leading moderate Andrew Bragg made clear he would not support policy or rhetoric that solely blamed migration for the housing crisis, telling this masthead there would be “economic consequence, moral consequence and maybe a political consequence”.

“We need to be very measured,” he said, noting that he did support lowering the migration intake.

On the other side of the party, LNP MP Garth Hamilton, a key backer of Hastie, advocated on Thursday to tie migrant numbers to housing development.

Asked about directly linking the migration and housing debates, Ley told Inside Politics that migration was “an important driver” of the cost of homes, but problems with infrastructure and housing were the fault of governments and “not the fault of any migrant or migrant community”.

Ley’s supporters finished the parliamentary year feeling more upbeat about her future as leader than a few weeks ago when her leadership appeared terminal, and will be looking for her polling numbers to turn around in the first part of next year to shore up her position.

Yet ongoing confusion about whether Andrew Hastie and Angus Taylor should challenge, Ley’s uneasy truce over net zero, and her more forceful tone in a media blitz and in question time have combined to create a glimmer of hope for Ley’s supporters.

Led by immigration spokesman Paul Scarr and home affairs lead Jonno Duniam, the party will in coming weeks release a set of principles on the levers it would pull to bring down migration numbers, an example being cutting the international student intake.

But the more hardline positioning of the Nationals and figures such as Price presents a risk of ongoing disunity.

One MP said: “The Nationals are obsessed with adopting the same intellectually corrupt views on migration as Pauline Hanson. And at the moment, the Liberals are too obsessed with keeping the Coalition together at the cost of our integrity and, in turn, social cohesion.”

McKenzie hit back, telling this masthead “it is not racist” to express legitimate worries about migration, which soared above forecasts after the pandemic. Prime Minister Anthony Albanese admitted in September that some “good people” attended the March for Australia rallies, even though they were partly organised by white supremacist groups.

“As leader of the conservative party of government in the Senate, we are on the side of Australians against powerful vested interests, like the universities, like big business, who are supporting the high intake of immigrants irrespective of the social and economic cost,” McKenzie said.

“Cheap putdowns of the Nationals also denigrates millions of Australians who are concerned about the economic and social costs.”

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