I have no issue with Churches offering sanctuary to illegals. The support comes from the funds provided by the congregation. All they can supply is room and board and food and these items will be in limited supply because most Churches are far from rich. Also it follows the commands of Jesus to 'do to the least of these' is to do as you would for Christ. Would anyone here deny food and shelter to Jesus?
I think the issue here is the word "illegals".
If churches make it their business to target support to illegals, rather than just Julio on the street, that's where the line is crossed, imho.
If, however, churches make no distinction between class, political persuasion, race, creed, ethnic origin, etc., etc., and provide food, clothing, and other necessities, that's perfectly fine.
I personally have worked with the Salvation Army and I see how they do it. They immerse themselves where the poor and destitute and, no doubt, illegals are. Their focus is not the status of the individual other than that person is hungry and needs clothing, perhaps even shelter. That person's needs are ministered to, and yes, they get a healthy dose of "The Word of God."