Is anyone here questioning the Mexicans' right to wave their flag? (Didn't think so). Your statement is akin to those constantly made by leftist anti-war protestors about their having the "right" to protest. No one is questioning their "rights," we're criticizing their actions. Understand the difference?
I think you've made a good point. The difference between an Italian flag being used in a Christopher Columbus parade or an Irish flag being used in a St. Patrick's Day parade versus the way the Mexican flag was used last week is that the Americans of Italian/Irish heritage aren't parading because of a reason that is directly hostile to the U.S. And, they aren't parading demanding special rights or amnesties for their group (although there might be some Irish-Americans begging amnesty from their spouses the next morning).
It's not unusual to go to backyard bbq parties where I live, hosted by BOTH hispanics and non-hispanics, and see the colors of the Mexican flag and/or little Mexican flag toothpicks, etc., used at a Mexican food-themed party. But, there's usually an American flag flying from the front porch. One local hispanic heritage organization (they do historical/genealogical stuff, etc.) uses American/Texan/Mexican flags in their special event centerpieces.
"Is anyone here questioning the Mexicans' right to wave their flag? (Didn't think so). "
To the contrary--a hell of a lot of people here were saying things like "get the hell out, if you want to wave that flag." So, you're wrong right out of the box!