Would you agree that the Catholic Church has an image problem? The causes aren't just third-rate novels like "The Da Vinci Code" or the "discovery" of "The Gospel of Judas," as if spurious ancient writings about Jesus Christ were something new under the sun.
No, the image problem is largely self-imposed these days. The Church's enemies magnify the flaws of her members, to be sure, but they did not instill those flaws, nor do they install those members into positions of power.
Primarily, the Church's reputation has suffered because of the priest sex scandals. I would argue -- I have argued -- that the laity share the blame, for insisting that their clergy be "nice," non-judgmental, and non-dogmatic. But the primary responsibility rests with the bishops who did very little to stop the problem, beyond moving offending priests into therapy or reshuffling them into different jobs.
The scandal, then, stemmed from bad governance. (If you think the problem was because priests can't get married, you came to the wrong blog.) Instead of confronting the problem and causing a temporary disruption, bishops opted for a "soft" approach that would not cause grave scandal to non-Catholics. The result was an even more grave scandal when the facts came to light. To those outside the Church, it looked like bishops were doing what was good for their "tribe" instead of doing what was right. And there was much truth in that assessment.
In light of that, non-Catholics will be forgiven if they think the bishops' defense of illegal immigration is just another cynical ploy. In this case, the prelates want to continue the flow of immigrants so they can increase the size of their flocks and wield more influence in society.
I do not pretend to know what goes on in the heads of the bishops, whether individually or collectively. Personally, I doubt that they are that coldly calculating, and they genuinely believe that legal and illegal immigrants should all be granted citizenship, showered with various forms of public assistance, and receive a gentle kiss on the forehead before going to sleep every night. But you can't blame the public at large for harboring doubts.