I’m not saying I’d do a full on Spanish accent (which I can do quite well!), but I’d definitely say “mexicanos” with the Spanish sound for the x. It’d sound weird otherwise. If I’m talking about the country, in English (“Once in Mexico, I…”) I’d pronounce it the English way, but if I’m ordering a meal and it’s got the Spanish adjective-noun order and is clearly a Spanish word, I’d pronounce it the Spanish way.
I try not to exaggerate it, but yeah, when I order enchiladas in a Mexican restaurant, I’ll pronounce it as “encheelathas”.
FTR, I’m not fluent in Spanish, but I can hold a conversation pretty well. I took it all the way through high school, and since I have family in Mexico I have spent a lot of time there.