Lots of people primarily identify by their religious affiliations. I think that's fair.
> Your sex and skin colour is given, your religion can change.
Ask a Muslim which will change first: their gender, their skin color, or whether Mohammed was Allah's prophet.
All that being said, your point about religion and race being separate categories is fair and well taken.
You are generalizing in a way that will create animosity. There are liberal people which identify as muslims.
Even though most religious people identify themselves by their religious affiliations, not all do, and not everbody is religious.
I think religion is a cancerous meme, that we shouldn't pay respect to. I don't even want to be asked whether I am religious, nor what religion.
My name allows a funny pun in that regard: I'm Christian, but I'm not.
> I think religion is a cancerous meme
My underlying point was that people with faith don't see their faith as a choice about the existence and character of their god (or other non-deist beliefs). It's not objective or accurate to say religion is different because it's a choice.
If anyone is offended by my point, I would challenge them to rethink their assumptions about how tolerant and accepting they are.