I think 'ethnicity' is a complicated term, since it's a catchall for all sorts of identities we can't quite assign to something easier to parse. In the example of the Australian Indigenous, that identity is a Venn diagram of overlapping ideas about lineage, culture, language, and tribal affiliation. Any one or more of those attributes could be potentially disrupted and yet maintain Indigenous identity and acceptance by the larger community - perhaps precariously.

A counter example would be the American designation of 'Latino' as an ethnicity, independent of race, language, and culture, and based entirely on national origin.