With race issues being so complicated right now, it is important to understand the meaning of race historically. Race is a social construct. Where we use the word race today, we should use ethnicity. Ethnicity is biological. If you use DNA today to trace your history it will tell you percentages of different ethnicities, not races. Your report will not say you are 40% White and 60% Black, it will be more like 40% European and 60% African, and usually more broken down by region. Race is socially constructed and most notably with whiteness. A society gets to determine who is white, which usually means who gets an advantage.
So, for the Gilded Age as Eastern and Central Europeans started flooding into our nation many who had olive skin and where Catholic, they were not considered equal to Americans and Western Europeans. What may sound strange to us today is that Greek, Italians, Jews, and others from those areas were never seen as white.