It would be an insult to them to lump Sunni with Shia. It would be an insult to lump Saudi with Palestinian or Somali.
The only sensitive thing is to recognize diversity and create 217 distinct new groups to be protected. To insult them would be insensitive.
The more recent immigrant groups (late 19th/early 20th century) went from being discriminated against and regarded as not really "white" to suddenly being part of the supposed elite who had caused all the country's problems since 1607.