Here's how to see what Facebook has assigned for you. In your Settings, tap the Ads tab and click "Manage the preferences we use to show you ads." Next, select the "Lifestyle and Culture" section. You might discover you've been tagged as African American, Asian American, Hispanic -- or maybe you don't have one at all. This seems to be the case for myself and several other white friends and colleagues, which suggests that Facebook doesn't assign an "Ethnic Affinity" for Caucasians.
Facebook's business model is built on giving advertisers and marketers the ability to microtarget users, so it's easy to understand why this would be a powerful tool. However, placing ads for housing or employment that exclude people based on race is super illegal -- and has been since the '60s.