I recently heard a convert say that he was an "American Muslim, in that order." I took issue with the point because it seems to force a collision between two ideas that needn't collide. It seems to say that if he had to choose only one, either American or Muslim, that he'd choose to be American. I don't even think most Americans would put their country above God. Don't they say "God, family, country," in that order?
Personally, I don't think the sequence of the words should extend their meaning. One might call himself an American Muslim to distinguish himself among Muslims from other countries, while one might call himself a Muslim American to distinguish himself among other Americans. The two terms describe different spheres by which a person can identify himself, and affect different parts of his life. You could say, for example, that a woman is a teacher and a mother, describing first her career path, and also her role in the home, while both make up parts of her identity.
Similarly, we can describe a person's identity without having to prioritize either nationality or religion. But forcing one to supersede the other undermines at least one of these components. In this case, Islam is undermined, as if the speaker were saying that he was only Muslim insofar as it was compatible with whatever he valued as being "American."
I consider myself to be an American Muslim (or Muslim American--whatever) without conflict. But I know that when I die, only one of these will matter, and that's my priority. In fact, I think that's what makes me a Muslim in the first place.