Hard to say. As you state, HT is almost completely mute on the whole issue of religion (except for the Mormons in Utah, the Jewish CSA propaganda minister, the corrupt Quebec collaborator priest, and the Jewish polititian from NYC). Not a single main POV character is specifically identified as Christian.
My speculation goes like this:
(1) One of the reason religion (Christianity) remained and remains so important in the OTL USA is because the US largely avoided the destruction and horrors associated with WW1 and WW2. Many Americans could still believe God is good and and that he/she/it looks with favor on mankind - or at least them.
(2) Also, in OTL, there was no successful CSA and hence no permanent division of the Christian Churches into separate Northern and Southern branches. In general, the Christian churches gradually became a supporter of civil rights and integration thru the whole country, further helping them survive in a more secular society.
(3) In HT's TL, you both had a permanent division of the country (and probably church structures), but more importantly, the US and CS fought 3 bitter wars between 1865 and 1945, with massive destruction, violent revolutions, holocausts, the rise of a nationalistic socialism in the north, racist fascism in the south, and millions of casualties. In this dystopian North America, it is reasonable to imagine American attitudes toward Christianity would mirror developments in Europe. Directly faced with a world of evil and war, Americans would become disenchanted with the church and faith in a supposedly good god who lets all this happen. As with Europe in the 1940's period, America would become post-Christian.
So, my theory is that HT hardly talks about Christianity because it is totally unimportant to his characters and he tells his story only thru them. Other than the Mormons and maybe the Catholic Mexicans, most people are probably essentially atheists in how they view the world.
By the way...it's great to see you back!