Immigrants rejecting cultural assimilation with the local population are unwelcome invaders by definition. Newcomers by rejecting adoption of the local culture, are disrespectfully asserting an unjustified claim to establish and impose a foreign culture. Such is an invasion, albeit short of armed conflict or what colonists euphemistically term 'annexing', but that is only difference.
Immigrants seeking 'a new life' in Australia or New Zealand have a moral obligation to respect and adopt the ways of life of the local inhabitants of Australia and New Zealand respectively, not to impose their previous ways of life upon their new hosts. It is for the host country to facilitate and support that assimilation, not to abandon people.