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The health minister, Greg Hunt, lobbied his cabinet colleague Michael Sukkar to include gender and sexuality questions in the census – despite the assistant treasurer’s intervention to have the politically sensitive questions dumped from the census test.

In a letter to the Victorian equality minister, Martin Foley, earlier in January, Hunt revealed he had written to the assistant treasurer in support of the inclusion of questions that would “greatly inform the government’s knowledge about the LGBTI+ population cohort in Australia in the 2021 census”.

Hunt’s support for the questions is significant as it is the first sign of division at the cabinet level as to whether to ask Australians their gender and sexuality in the upcoming census.

Gender and sexuality questions were among eight potential new topics identified by consultation in 2018 and were set to be included in a census test late last year. In October Guardian Australia revealed that the Australian Bureau of Statistics had dumped the questions from the test after intervention from the assistant treasurer’s office, prompting a backlash from stakeholders including the LGBTI Health Alliance.