Good example, though I chose Africans Americans to illustrate my point that fighting side to side against a common enemy (though it may change the opinions of those directly involved in the conflict) does little to advance racial equality.
I'm not fully aware of the situation back then since my knowledge of history its quite limited, but the case and how relates to Mexicans has some differences. To put it simply, you can't tell that someone is a catholic just by looking at them, however you can with races. The issue; while dividing, still allowed for the coexistence of both groups whilst they where vying for power with one of them in secrecy (the catholics). Foreign as the powers may be, Spain and France would had encountered a large support from the British catholics and may had made their house quite easily if they had succeeded. This is brings to relevance the fact that when conquering differences in culture matter, aside from a few quirks westerners are not all different. Which would had made the transition easier, which has never been the case when differences of races or culture (e.g: Jerusalem).
Racial profiling test, when they ask for a Muslim do they want a Nordic, blue eyed, blonde or a Middle easterner? Ethnicity, culture, religion they are all part of the idiosyncrasies of a people and aren't completely separate for even for an objective study one must look in reference to the others.
Plus I'm sure that by Muslimization he actually meant immigration.