I just want to start out by saying that I am not a race denier.
I believe, from an anthropological standpoint, that there are only three races. There is the Caucasian race, the Negroid race, and the Mongoloid race. Although originating in the Caucasus Mountains, the Caucasian race consists of white Europeans, Arabs, and East Indian (both dark skinned and light-skinned). The Mongoloid or Asian race includes the Japanese, Koreans, Chinese, Filipinos, Indonesians, and what we would term American Indians. The Negroid or Africoid race involves Sub-Saharan black Africans. However, the Australoid race kind of defies a racial category because they have a similar phenotype as Africans but are not considered to be Negroid.
Then, there are people who are legitimately of mixed race. Many Latinx peoples are mestizos mixed Spanish and Indian descent). Some are even mulatto (mixed black and white) like Dominicans. I think East Indians are a Mediterranean Caucasian people with a strong Australoid admixture. Filipinos are a Mongoloid people with Negrito/Australoid admixture. Polynesians are mixed Melanesian/American Indian-type Mongoloid.
Jews are not a race, even though most people think of them as an ethnicity.
Judaism is a religion.
Most Jews, racially, are Caucasian.
But, America does not exclusively define race by DNA or biology. For instance, take the one drop rule. The one drop rule says that a person who has any black in their DNA is considered black. I, like many ADOS families, have some people in my family going way back who look white. It does not matter if the person is over 90 percent white and has a predominately white phenotype. On the other hand, many Hispanic mestizos are technically considered white even though they are of partial indigenous blood. Many of them don't look white. White people don't think of them and treat them as white. And a lot of them don't see themselves as white. But, some of the assimilated ones would like to be thought of as close to white as possible.
Some people in Sub-Sharan Africa don't look at black Americans as being black because they are so mixed and admixed with European blood.
So, race is more socially constructed in America than it is in other places.