I think the reasons for at least some of them are quite nefarious, with the others just following along like obedient little lap dogs.
In a nutshell, when border-crashers are caught by ICE and other security personnel entering our country illegally and with children, procedures may involve the separation of the children from the adults who are bringing them along. Note that I did not automatically imply familial relationships for too often they don't exist. The LA Times, no bastion of conservatism, has noted the problem. Rather than reinvent the wheel, I'll post now the video of a press conference on the matter given by Homeland Security Secretary Kirstjen Nielsen and continue my remarks below the video.
Note how she emphasized the concern for children who might well be being exploited (sexual and otherwise) by the adults who accompanied them. This is not a new problem. Two years ago, the Washington Post (hardly a conservative news outlet) noted that then-President Obama released thousands of these children to adults who were not vetted and who may have been sex traffickers. Was this simply gross negligence on his part? Maybe not!
I will now link to an article that seems unrelated, but may not be. Inspector General Michael Horowitz, while investigating corruption at the Justice Departent and the FBI in relation to Hillary Clinton's email security violations, came across evidence that she may be involved in sex trafficking of children.
Might this be a good part of the reason why the libs are objecting to "parents" being separated from their "children" at the borders? Perhaps they know damned well that kids are being trafficked and they want the children to stay with their "handlers" lest the children elude their grasp.
The US bishops' gab-fest ended this weekend. They spent most of the time whining about the President's enforcement of reasonable immigration laws. Of course they did so at the behest of their Democrat puppet-masters and sugar-daddies. They know on what side of their bread the butter appears: millions of federal dollars to "resettle immigrants). Let's see if we hear of any more blather about "canonical penalties". I wonder if the frivolous threat of "canonical penalties" is its own canonical offense.