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.
Facebook maintains that what it's doing is above-board because it never asks users to specify their racial identity. Furthermore, it makes an adamant distinction between "Ethnic Affinity" and race, insisting the former is simply based on pages you have liked and engaged with. Curiously, though, if the affinity it's assigned doesn't seem right to you, you cannot change it. Why? Doing so could be construed as confirming one's racial identity -- which then makes the case that Facebook was facilitating an illegal, exclusionary advertising platform.
Here's the good news: If you're at all uncomfortable being targeted based on whatever Ethnic Affinity it's tagged you with (if it has at all), you can simply remove it from your Ads Preferences section by hitting the "X" while hovering over it.
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