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.