I'm surprised people think it should be that easy to separate race, gender, communal identity, and beliefs. Yes, religious belief is a choice, but discrimination on the basis of religious belief is impossible unless that belief has been expressed somehow.
Let me give an example. I'm not a Muslim. My grandmother (also not Muslim) is from a Muslim country. She covers her hair with a scarf, what you might call a "babushka scarf", even after living in the U.S. for years. I never thought of it as a religious statement, I don't think she or anyone else that knows her does. It wasn't prescribed by any religion that she believes in. It is, quit simply, standard dress for women in the neighborhood she's from.
But she could not teach college in Turkey wearing that babushka scarf. She would probably be "profiled" as Muslim in airports for wearing it, because she has a "Muslim" name and brown skin. Is that racism? Maybe in a very trivial way, but I think it's very clear that the thing people who would mark her as "Muslim" are concerned about is Islam--a creed--and (let's be generous, because for some of them this will be true) only what they believe to be her creed. It is not ultimately about her race/phenotype/racial characteristics.
Is it not an act of--if you'll indulge me a bit--cultural violence for her choice of dress--one which is shared by a vast number of women from all over Asia and Europe--to be a pretext for being treated differently? Just because, technically, she chooses to wear a scarf over her head, does that alone justify all these consequences for it?
I think this is a pretty clear case where a kind of "credophobia" is at work. Overzealous attempts to monitor a particular creed result, in the U.S., Turkey, and many other countries, in a kind of cultural coercion that I hope we would all be uncomfortable with. Even if you are completely justified in your dislike of the beliefs involved, the result of acting on them in a public, general way, looks, walks, smells, and sounds like a cultural prejudice.