In What Religion Looks Like, Wisconsin Edition, Kim Bobo reports that most of the state's most high-profile religious leaders offered public employees early support. Among those leaders was the Right Rev. Steven A. Miller, the Episcopal Bishop of Milwaukee, who wrote:

I believe we can all agree that our baptismal vow to “respect the dignity of every human being” is not served by a majority simply pushing through legislation because they have the votes necessary to do so. As Christians, it is our duty and call to make sure that everyone has a place at the table and every voice has the opportunity to be heard. Respecting the dignity of every human being requires taking the time to have honest and faithful conversation that respects the rights and freedom of all.

More recently, however, Peter Laarman, has argued that organized religion's support for organized labor is fairly tepid, and has been for several decades. Among the reasons he cites is this one:

Identity politics among religious liberals: The Christian Century review of Winner Take All Politics quotes the authors’ spot-on analysis of progressive religious leaders’ conspicuous lack of interest in worker struggles in recent decades. In a word, these leaders had other priorities: women’s rights, LGBT issues, environmentalism, etc. “The result,” say Hacker and Pierson, “was a boon for the post-materialist causes of more affluent liberals, but it left traditional material causes with only a handful of energetic backers.” I couldn’t put it any better. In my own work, I am sometimes asked why I, as a gay clergy leader, remain so committed to worker issues. The implication: Don’t I know what’s really important?

Meanwhile, supporters for unregulated capitalism are developing a theology of their own. They believe God hates unions, and opposing them is holy work. Peter Montgomery sheds some light on their thinking:

One of the most striking examples of this theory reaching into the political realm is found in an early Christian Coalition Leadership Manual, co-authored by Coalition founder Ralph Reed in 1990. A section titled “God’s Delegated Authority in the World,” which argues that “God established His pattern for work as well as in the family and in the church,” cites four Bible passages instructing slaves to be obedient to their masters, including 1 Peter 2:18-19:

Slaves, submit yourselves to your masters with all respect, not only to those who are good and considerate, but also to those who are harsh. For it is commendable if a man bears up under the pain of unjust suffering because he is conscious of God.
And then, the astonishing lesson drawn by Christian Coalition leaders from these slaves-obey-your-masters passages:

Of course, slavery was abolished in this country many years ago, so we must apply these principles to the way Americans work today, to employees and employers: Christians have a responsibility to submit to the authority of their employers, since they are designated as part of God’s plan for the exercise of authority on the earth by man.

Slavery also makes an appearance in “Indivisible,” a booklet of essays being aggressively promoted by the Heritage Foundation as part of its campaign to assert that genuine fiscal conservatism cannot be separated from social conservatism. In one essay, anti-gay activist Bishop Harry Jackson writes that minimum wage laws “[remind] me of slavery.

Bishop Jackson might benefit from spending some time with Rerum Novarum.

Pope Leo XIII had a few things to say about "The Condition of Labor" in 1891, including this:

48. In the last place, employers and workmen may of themselves effect much, in the matter We are treating, by means of such associations and organizations as afford opportune aid to those who are in distress, and which draw the two classes more closely together. Among these may be enumerated societies for mutual help; various benevolent foundations established by private persons to provide for the workman, and for his widow or his orphans, in case of sudden calamity, in sickness, and in the event of death; and institutions for the welfare of boys and girls, young people, and those more advanced in years.

49. The most important of all are workingmen's unions, for these virtually include all the rest. History attests what excellent results were brought about by the artificers' guilds of olden times. They were the means of affording not only many advantages to the workmen, but in no small degree of promoting the advancement of art, as numerous monuments remain to bear witness. Such unions should be suited to the requirements of this our age - an age of wider education, of different habits, and of far more numerous requirements in daily life. It is gratifying to know that there are actually in existence not a few associations of this nature, consisting either of workmen alone, or of workmen and employers together, but it were greatly to be desired that they should become more numerous and more efficient.