" they almost certainly will suffer from diseases relating to malnutrition, lack of genetic diversity, and tropical parasite-borne diseases"

Or maybe not.

Malnutrition is caused when a population grows and outpaces its resources. If the population has been stable all this time, they are probably ok, food-wise.

Lack of genetic diversity may not be a problem if they get occasional infusions from people on neighboring islands, out on fishing expeditions.

Tropical parasite-borne diseases could be countered by local genetic features that provide immunity (similar to the sickle cell trait vs malaria?) and/ or by indigenous medical practices.

Who is endangered?

They've been there 10000 years, and still going strong. We've been around only a few thousand years, are plagued by the social problems that come with overcrowding, and headed for environmental catastrophe. When we've finally bombed or poisoned ourselves into oblivion, it will be isolated peoples living in their traditional ways that will carry on the heritage of humanity. "The meek shall inherit the earth" - Jesus