In the past, some language centres have had trouble registering for Deductible Gift Recipient (DGR) status. To receive DGR status organisations must have a charitable purpose that is for the benefit of the public. Language centres should no longer have trouble getting their charity, PBI or DGR status recognised.
In 2014, the Australian Charities and Not-for-profits Commission (ACNC) was established as the independent national regulator of charities. That year, the ACNC released The Commissioner’s Interpretation Statement: Indigenous charities. In line with this statement, Aboriginal and Torres Strait Islander language centres meet the public benefit test as they are working to address disadvantage. You can read the statement here: https://www.acnc.gov.au/ACNC/Publications/Interp_IndigenousCharities.aspx
Information of specific to language centres, compiled by First Languages Australia and the ACNC, is published as page 51 of Warra: Building teams, building resources.