One of the most obnoxious refrains you hear when you complain about Islamophobia in the United States being a form of racism is “Islam isn’t a race, it’s a religion.” It’s a nasty derailing technique that’s endorsed by luminaries such as Richard Dawkins.
And it’s wrong for transparent reasons. You don’t need to look far for other examples where religion and ethnicity are conflated within the logic of prejudice. You only need to look as far as the Holocaust, the single bloodiest genocidal campaign in history, which targeted anyone of Jewish ethnic descent regardless of what religious beliefs they professed, based on stereotypes that explicitly invoked biological, racial difference.
You don’t need to look far in our own time to find people being targeted for “looking Muslim” regardless of their racial beliefs, and indeed, you can find Dawkins’ fellow luminary Sam Harris openly endorsing racial profiling as policy.