An understanding that I find credible is that at the time, circles within circles existed in the French army, to keep practicing & devout Catholics out of the officers' corps. The fear was that their loyalty to Rome transcended that of faith and morals. The affaire des fiches, in the early 1910s, during the course of which it was revealed that a NGO outside of the army had or had access to files on all the soldiers whose main content was their religous beliefs come to mind. In the time of Ultramontagnism and the like this was a prudent, if very controversial, policy.
Anyway, the gist of this alternative explanation is that there was clear evidence that someone had been selling out aux Boches, and the politicians demanded that someone go to Devil's Island. The perp, being a member of this unofficial army within an army whose protection went all the way to the top, threatened to spill the beans, and thus someone else had to be a fall guy. Captain Dreyfuss just happened to be semi-plausibly linkable with the crime, less-connected, and have a German surname.
Rather than to open the can of worms of an unreligious republic having circles within circles to prevent a "Catholic" takeover, Dreyfuss' defenders, rightfully aghast that an innocent man was found guilty, chose, in the spirit of the times, to portray his struggle as part of the struggle for Jewish emancipation, which it was not.
The idea of having a reactionary pope of the likes of Pius X, installed at the request of the Habsburgs, command his minions in the French government gives me the shivers; I can comprehend at that time the need for religious discrimination. I do, however, wonder at the same time, if World War 1 would have been the same senseless meat-grinder had there been Catholics in the officers corps who had the informal means to confer with their counterparts in the other armies, and declare que ca suffit! France's victory in that war was greatly Pyrrhic.
In my opinion, it is not an irony of history, but a correlation of cause and effect that Pius X, installed against the wishes of the conclave during a time of anarchists, lived to see the war that would destroy the empire whose mouthpiece he'd been erupt. His kingdom should not have been of this world.