They were allowed entrance into the country of Mexico. I would now consider them to be legal residents of the country of Mexico. They are no longer persecuted as they were allowed to enter the country of Mexico.
Best view expressed on these pages yet!
Even with LEO personnel posted every few yards, if they rush the border some or many will continue to make it across to protected legal status. If we fail to eliminate that status by legislation, we will have very few "civilized" means of resolving the issue, if any.