That probably depends from state to state and the political history of each country, as well as which are the most dominant factions within Syndicalist countries.Also how would syndicalist nations treat religion. I know in the CSA there is a blurb about Dororthy Day and the Catholic worker movement, so I assume there at least is freedom of religion and militant atheism might not be a thing in the CSA.
Totalists are totalitarian, so they'd want to control every aspect of life. This generally leads to conflicts with religious authorities because totalitarian ideologies try to mold the faith to support their ideology or actively try to suppress it if they can't. With Marxism having a certain influence too, you can also expect some sort of state atheism given on how they interpret "Religion is the people's opium".Also in regards to religion, are there differences among certain kinds of syndicalists in regards to religion? Like are totalists more in the vein of state atheists where as your progressives are relatively tolerant of faith?
For other brand of syndicalism, it probably depends on the local political landscape. In most countries religious authorities were seen as aligning with right-wing forces, so they probably wouldn't be that popular in Syndicalist movements. But you also have had cases of left-wing believers that could have created their own brand of syndicalism. I even think among the Papal options in Kaiserreich, one of the possible Popes is very sympathetic to the syndicalist cause.
Catholics are probably going to suffer a bit in the Commune of France because the French left generally was opposed to the Church, for historical reason as the Church wasn't originally favorable to the French Revolution which the left-wing puts on a pedestal. The fact you also have a faction that calls itself Jacobins speaks in that favor, considering who they are modelling themselves on.Also, do certain faiths get hated on more in certain countries? Like are syndicalists in Britain going to hate the C of E but are more okay with nonconformists, or are Catholics going to be persecuted in Syndie republics in France and Italy?
I imagine you have similar situations in other countries.