He was in a fit of rage and he just got the news that his son had died. He was killing the two asshats that killed his son. Surely the mexican people could understand that.
And Ilene was just getting revenge on the guy who put her daughter down. They had a rule. Travis broke it almost immediately, and mortally wounded Oscar in the process. From their perspective, he was dangerous. They don't know the backstory we know, so they're not going to just excuse his behavior. It might have been better if he hadn't killed Oscar, but even then, he went savage on those guys.