Correct. A large part of what caused them to turn was the anti-Catholicism at the time. The Mexican government and society encouraged their desertion by emphasizing the Catholicism of Mexico, along with offering bounties for them to come over to the Mexican side.
The San Patricios was probably the most hard-hitting, hard-fighting unit in the Mexican Army, but then they had a reason to be: when captured, a number were executed for desertion. The last stand of the San Patricios in Mexico City was particularly bloody ...
Went to the wikipedia entry. What a story. Largest mass execution by U.S. San Patricios still honored in Mexico today. Santa Ana smarter than given credit for.
All I knew before now was that they carried Brown Bess flintlocks as in War of 1812.