Do you know of any types of parents (race, nationality, medical history, diet, etc.) who never or almost never have autistic children?

No: Studies have shown that autism cuts across race, socio-econimc status, nationality, and most other measures. Several large-scale studies are underway to look are specifics of maternal behaviors such as diet and exposures during pregnancy, but no results yet. There is a clear genetic contribution, so those with a history of having had an autistic child are at increased risk.