What "non-ethnic" immigrants do you have in mind?
I for example am of Scottish, Irish, English, German, Dutch and Scandinavian ethnicity.
Dictionary
Definitions from Oxford Languages
eth·nic·i·ty
/eTHˈnisədē/
noun
the quality or fact of belonging to a population group or subgroup made up of people who share a common cultural background or descent.
"the interrelationship between gender, ethnicity, and class"
What immigrant groups are you thinking of who are not ethnic people?