I'm Part Mexican, my girlfriend is half Mexican, her daughter is a quarter Mexican.
We're all proud of our culture, however If I were in Mexico I wouldn't fly a Us flag over a Mexican flag, and I wouldn't fly a Mexican flag over a US Flag in the US, though the man is a patriot, but he should have left that in the hands of the police since it's illegal, but to be honest his emotions made him look a little crazy, and his emotions are partially fueled by ignorance, pardon me for saying so but being patriotic to your country of origin does not automatically place you under the category of being an illegal immigrant.
IMO both the owner of the bar and the man who removed the flag were both wrong.
The owner should have either flown the US flag over the Mexican flag or on another pole of equal or lesser height.
The man should have contacted the police and had the authorities handle the situation.