A Liberal senator has broken ranks to criticise Angus Taylor’s plan to bar non-citizens from accessing welfare, warning it will create “two types of members of the community” and is “not the Australian way”.

The outspoken backbencher Andrew McLachlan said migrants should not be blamed for economic problems including the housing crisis, and warned his party’s immigration rhetoric was alienating diaspora communities.

The opposition leader brushed off his colleague’s concerns as he defended the use of the phrase “mass migration” to describe the rate of overseas arrivals.

“It [the rhetoric] only alienates the government that has got it wrong, this is nothing to do with [migrant] communities,” Taylor told reporters on Tuesday.

Taylor made immigration a centrepiece of his budget reply speech last week. He promised to dramatically reduce the temporary immigration intake by tying it to housing construction, and to restrict the national disability insurance scheme and 17 types of welfare programs to Australian citizens, if the Coalition wins the next election.

That would bar migrants – including permanent residents – from jobseeker, the age pension, disability support, parenting payments and the NDIS, even if they paid tax.

The announcements caused unease among some Liberals MPs who now believe One Nation’s Pauline Hanson is dictating their party’s agenda.

Speaking on ABC’s RN Breakfast on Tuesday, McLachlan warned that Taylor’s citizen-only welfare policy risked creating a two-tiered society.

“I have deep concerns coming from a multicultural community that we are going to create two types of members in the community going forward with this policy suite,” the South Australian senator said. “I’m not sure it leads to a healthy Australian community.

“If you’re both contributing to the wealth of the nation and [only] one is entitled to certain entitlements, you could have almost a form of a strata-ing of our society.

“I’m not sure that’s the Australian way, or what our communities want.”

McLachlan said the Coalition’s rhetoric was alienating migrant communities, who have abandoned the Liberal party in droves at the past two elections.

“I don’t think we should take a negative approach to migration. Certainly, it should be controlled, and we don’t want to invite people here without giving them a society that can accommodate them both economically and culturally, but we cannot continue to blame migrants for the problems of our economy.”

Migrant groups last week condemned the Coalition’s policy as “a dangerous escalation of dog-whistle politics that targets communities of colour” rather than a serious answer to the housing crisis.

“We are not in Trump’s America,” said Noura Mansour, the national director of Democracy in Colour.

Coalition frontbenchers have argued that the welfare ban, which would not apply to people already accessing the payments, would incentivise migrants to take up citizenship.

Gaining Australian citizenship requires someone to have been living in Australia on a valid visa for at least four years immediately before the day they apply, meaning that even aspiring citizens who begin their application as soon as possible could be without help for at least four years.

Some countries including China do not recognise dual citizenship, meaning applicants would forfeit rights in their home nation after taking the pledge in Australia.

Taylor defended the policy on Tuesday, arguing it was in the national interest to “put citizens first”.

“Citizenship matters in this country and we welcome those who commit to citizenship, we will commit to them,” the opposition leader said.

The internal stoush came as a parliamentary inquiry into skilled migration heard warnings that slashing the intake would cause a crisis in the care sector.

“Migrants didn’t cause the housing crisis and reducing migration isn’t going to solve the housing crisis, but what it will give us is a care crisis,” Leah Williams Veazey, a sociologist at the University of Sydney, told a hearing on Tuesday.

“We already have incredible shortages of doctors, nurses, physiotherapists and other allied health workers.”

The Business Council of Australia last week also warned that significant cuts to migration could worsen existing workforce shortages.

The minister for multicultural affairs, Anne Aly, accused Taylor of casting permanent residents as “unworthy” and a “burden” on the country.

Anthony Albanese said Taylor’s budget reply announcements were focused on “fighting One Nation”.

“We need to not seek to divide Australians, we need to seek to bring Australians together,” the prime minister said.

McLachlan also sent a warning to Liberals considering switching allegiances to One Nation after their former colleague Hollie Hughes and the former party vice-president Teena McQueen joined Hanson’s party.

“You’re making a mistake,” he said.

“If you want to share Liberal values, then you shouldn’t be looking for a false path and a wide path, which does not contain policy that will advance Australians’ lives.”