Only if they have the particular bad genes.
Everybody has a genetic weakness of some kind only they are not expressed.
Most genetic weakness goes unexpressed because a person has only received that bad gene from one parent.
When a person receives the bad gene from both parents the genetic disease is expressed.
Diseases such as hemophilia (Europe’s Royalty) and sickle cell anemia (African Americans) are such genetically transmitted disease.
These diseases become prominent when isolated populations of small numbers interbreed.
Europe’s royalty and African Americans haven’t died out because there numbers are in the thousands and millions respectively, but this tribe’s numbers are far too small to be sustained with out an influx of outside genes. A number I seem to recall reading is about 50,000 for a minimum sustainable breeding population.