OK, let's slice your nuances thin and be more specific.
They advocate an amorphous religious state in which the state benevolently allocates justice and resources based upon the needs of the people, and grounded in Biblical principle.
Statist, Fascist or Communist...they're all the same to me and my mortal enemy.
How do you like living in the United States of Morgan Stanley, Frank, and Dodd?
So, there were Catholic intellectuals who were in favor or a different balance of state, corporate, and individual, power. Many a Protestant was a Fabian socialist in the same era, too, so it's just another example of intellectuals doing their usual theorizing. There are more than enough boneheaded ideas that were once popular among one or another group of intellectuals to find fault with any religious group. Just put this theory in that category and forget it, no one much is even interested in hearing about this theory much less in implementing it.
You have no reason to fear some "mortal enemy" creeping out of a dark, dank, Catholic, alley somewhere. The existing Protestant system is heading quite rapidly to the logical endpoint of Protestant theology overlaid on a society. Rest assured that Catholics don't want to seize control and take credit for the existing system. What we have now has done a fine job of destroying the Constitution in favor of the Almighty Dollar. Those who built the skeleton and left it to be fleshed out by future generations are long dead, and those rapidly establishing a fascist nobility are cozy in their Snuggies oblivious to everything except their own superiority
Regards
What you must understand is that Distributism is an economic application of Subsidiarism; it’s antithetical to state management of justice and resources... which is why distributists have had a difficult time forming a political movement. All stripes of politicians recognize it would strip them of power.
The only sense in which the government “does” anything for Distributism is that it pulls back from its role in protecting the market shares of behemoth corporations, by means such as reducing regulation, withdrawing from market management, removing a tax structure which favors supply line dominance, reforming intellectual property rights (which are supposed to support innovation, not destroy it), and prevent exclusive contracts. You’ll note that the first four of those five are downright libertarian.