The problem is that you are considering self-identification. But what really matters in the real world for racial/ethnic discrimination is what society identifies you as, not what you identify yourself as.
It's not about your beliefs when the TSA pulls you out of line for secondary screening. It's not about your beliefs when you have to walk around on the street after 09/11 and people stare at you.
I knew a guy who was a North African Christian. Society sure viewed him as Muslim though when they saw him in an airport, on a train, etc. I mean that guy could have a bomb. He just looks like a Muslim extremist.
After 09/11, Sikhs were attacked for looking Muslim. Obviously their beliefs are totally different. But they look close enough to Muslims to attract hate crimes from racists.
There is definitely a pretty significant racial component to being Muslim in the West.
I am a white dude. When I walk around with a Jewish friend, society is not viewing us as white + Jewish. We are just two regular white dudes. Nobody knows he is Jewish unless they get to know him personally.
When I walk around with a Muslim friend, everyone sees us as white + Muslim. It's just a social inference that happens instantly, unconsciously, by just about everyone.
I am arguing the opposite. If somebody says they aren't a Muslim, they're not a Muslim. I would think somebody an idiot of the highest caliber if they think an Egyptian Coptic Christian, or a Lebanese Maronite, is a "Muslim" (except in a very complex theological sense I won't bore everybody with ... ). 99.999% of people would think the same. They might *initially assume a copt is Muslim based on looks*, but if the person told them they were Christian, they wouldn't somehow think that's impossible or a contradiction, ZOMG a Middle Eastern Christian, nobody has ever heard of such a thing. There are assloads of Middle Eastern Christians. Millions. I really don't believe there's anybody so ignorant as to insist they are actually Muslim, even when they are claiming to be Christian.
Everybody is quite spectacularly clear that if they follow non-Muslim religions they aren't Muslim. Including those Muslims who, under the guise of takfir, are furiously identifying non-Muslims and slaying them by the assload as we speak. Even when they self-identify as Muslim, such as Shiites/Alawites/Ahmadi etc. Muslims themselves are quite monumentally clear that being Muslim is defined by your *religious belief*, not by ethnicity or race.
Witness the Western furor over the Muslim decimation of Christians in the Middle East right now. It's not like people's heads are exploding "wait, how can there be Christians in the Middle East, they are the Muslim race, who are these Christian Muslims." The whole idea of "Christian Muslim" is laughably, laughably ridiculous. And that's because everybody knows these are religions, not an intractable ethnic identity + a religious belief.
So yeah, you're certainly correct that people often *assume* your average Middle Easterner is Muslim. Statistics. But you can't take that assumption and then assume that people go around assuming there is a "Muslim identity" which attaches to individuals apart from their religious beliefs. They are just *assuming* the person probably holds Muslim religious beliefs. If it turns out they don't, they plainly aren't Muslim. Likewise, when a white guy turns out to be Muslim (like one of the guys I train judo with), it's somewhat surprising, but if the guy is serious then not for an instant does anybody then think "you are actually not a Muslim." That would be sensationally offensive and ludicrous.
I will grant that most people seem to think Sikhs are Muslims, and that's largely because nobody knows what Sikhs are, they think they are a variety of Muslim like Sunni/Shiite/Sikh/Sufi etc. This is pretty sad since Sikhism is a really cool religion that deserves more press.