Why Is Australia So Strict On Pet Imports?

They have many many unique native animals that can easily be threatened by disease or predatory hunting that can never be replaced.

ask Barnaby joyce

I think all the countries are.  

Because someone smuggled in a Basset Hound puppy and it devastated their ecosystem. 

Australia, like the UK, is protective of their existing speces and being an island, they are able to make sure imports don't bring in disease they don't have there.   And the same goes for food being brought in.     I don't blame them in the slightest.

Because they are an island that lacks the predators and diseases that other places have.

Because many (most) introduced species have caused severe impacts on our fragile ecosystem and oet owners are bad at containing their pets.

You mention kinkajous. These would , if allowed to escape, compete with possums and gliders, many already threatened, endangered or close to extinction due to predation by feral cats/dogs/foxes and habitat destruction. Particularly following recent fires.

Hawaii is worse.After several issues with invasive species, they now have strict import/export laws.

Zero cases of rabies, even with all the bats there.

Rabies free and we wish to keep it that way. 

Prior history... look up impact of Rabbits and Camels on environment.