19th century nativist anti-immigrant movement in US did racialize Europeans, particularly those from eastern and southern Europe who were of darker skin than earlier immigrants from northern Europe... as John Higham writes in _Stangers in the Land: Patterns of American Nativism, 1860-1925_ (1988), they were attacked as 'races of...the very lowest degradation' (p. 95)...
but despite the often virulent anti-immigrant sentiment and eventual restrictions imposed on immigration, the political rights of white ethnics (term encompassing wide range of groups who for much of US history did not identify as single 'white' group) were never in serious peril...they were eligible, for example, to become naturalized citizens after 5 yrs and some states granted them voting rights as non-citizens (with regard to politics, ethnic/national identity was important to 'political machines' that appealed to voters and offered patronage along such lines)...
very different experience/history for Chinese who were prohibited from entering US by racist congressional legislation in 1882 (such laws were kept on books until 1943) and were denied opportunity to become eligible for naturalization until 1952... Michael Hoover