Catholic priests were leading figures in the beginning of the Mexican War of Independence.
Later, professional soldiers took over the war effort and succeeded in achieving independence. Iturbide, the first individual ruler of independent Mexico, kept conservative clerics in his inner circle during his short rule. Religious doctrines can be deployed to support any kind of policies, but I'd expect collaboration like this from ranking members of a state church, more than violent uprisings.
Why were the churchmen so prominent in the independence struggle?