About 14% of Cuban immigrants report that they are not religious, compared to 7% of immigrants from Mexico.
The general story in the New York Times argues that America makes people more materialistic. This is likely to be true. Still, that doesn't explain why the Cubans and Mexicans would respond to the new environment so differently.
Two ideas seem likely to me. First, Cubans are less religious to begin with, from decades of socialism. Second, Cuban immigrants are more likely to be middle class to begin with than Mexicans, and therefore start further on the road to irreligion. I incline to the latter view.