The first amendment does apply to the rioter with the flag but it also does to the people watching this. The watchers will get inflamed by (a) the vandalism and (b) the spectacle of the Mexican (or any foreign) flag associated with the vandalism. They absolutely have a right to get angry.
I recently naturalized as a US citizen. It took ~15 years (permanent residency + citizenship). That was after spending a decade (multiple programs) here as a student. No one should suffer and live in fear in an ideal world. At the same time, it is galling to see the left support illegal immigration because (a) someone "contributes" to the economy, (b) they are paying taxes (how is this known by anyone except the payer and the IRS?), (c) they are good people.
The reaction of my extreme-left wing friends is to say "well, you got to come here. They deserve the same opportunity." I am the first one to admit I have had some advantages. At the same time, every legal immigrant goes through a relatively rigorous process. Any whiff of a criminal record has the potential to derail the process, as should be the case. Just apply the law equally to everyone. That's one of the promises of our constitution. I mean this both for liberals and conservatives. If a law is unjust, we have mechanisms in place to overturn them. But to ignore the law is a long-term danger to this country. This is one of the reasons there is a lot of support for this type of action. It is borne out of frustration. Lastly, the idea that people supporting deportation are racists is an easy cop-out to not have to explain how we got to the current state (saying this as a non-white person although I also disagree with the left's assertion that only white people can be racist).
It's weird that you won't come out and say what you think is "going on" though. I've given the explanation that the vast majority of people waving Mexican flags in LA would give: they are expressing that they're proud to be Mexican, or of Mexican heritage, and are sick of being treated like they're less than other people because of that heritage.
What is your explanation? I suspect that it's something along the lines of: "people waving foreign flags are signaling their intention to invade the US", but that you don't want to say it overtly because it's obviously a racist talking point from right-wing media.
I'm confused, you consider yourself quite liberal but you think it's bullshit for Mexicans in the US to celebrate their heritage?