Interestingly you've left it somewhat ambiguous as to whether you view these immigrants as morally upright while being somewhat naughty. You could certainly say that they've found an exploit/hack in the system by claiming asylum and could view that as clever and/or immoral depending on the eye of the beholder.

I will say that I don't think the situation is being handled all that well (and I suppose hasn't for decades, but perhaps that just goes to show that there's not much we can do at all), but as a resident of South Texas, I haven't felt any actual problems with my day-to-day life that I can directly attribute to illegal immigration.