The situation in Bohemia is complicated. While the majority is nominally Catholic, there is deep suspicion of the organization itself due to the actions of Austria-Hungary.
Okay, refresh my memory. IIRC A-H splintered after a victorious First World War (and since I only started reading the story after that I couldn't place my objection on that AH trope, but well...).
So it's been 'just' the Archduchy of Austria for over half a century by now? Or did I miss something concerning Hungary? Because Bohemia breaking away, but not Hungary would be odd.
While yes, Catholicism and the House of Habsburg had a close relation, and religion was an important element to their rule, I can see the topic not being easy.
Though again, it's been half a century. If not earlier, I'd expect at the very least with the independence of Galicia from Poland, that there will be a nostalgia wave concerning the old Empire. (That is if the Habsburgs hadn't managed to mess up in Austria itself). I'd very much expect film very much in the vein of the Sissi ones OTL to turn up (though under very different circumstances from the OTL '50s - Austria hadn't just regained it's independence from Germany and the occupying Allied powers)
So yeah, religion will be in the centre of an identity conflict there.
1. First you have the old Habsburg Catholicism, something that is to be left behind, the old oppressor maybe even (depending on how much the exiles got their part in writing the national history, I'd expect their influence to be somewhat less than OTL. I'd very much doubt that Germany would accept the politicians who lived as government-in-exile in Paris a say, or the ones that fought in the Czechoslovak Legion against them, after Bohemia joined them.)
2. Then we have Prussian Protestantism as the counterforce, the old conflict that haunted the HRE since the Reformation. The northern neighbour, modern, victorious, not in chaos (that they probably weren't innocent in creating). I'd be seen as a chance at first, but increasingly also as a foreign element, especially under the influence of...
3. Polish Catholicism. Yeah, those. Pan-Slavism, a perceived second class role behind the German Kingdoms and a religion to unify them. Though it didn't seem to have taken nearly as much as over there to the point of basically revolt, but the influence was certainly felt. And once the Poles failed, well that left, three options. Either returning to a Austria-nostalgia or...
4. Their other neighbour, the other big German catholic power - Bavaria. We've certainly seen them trying to take the counterweight in the old north-south, protestant-catholic tensions from Austria, until the king moved himself into the difficult position of bringing dynastic ties into the whole thing.
5. Leaving the chance to actually strengthen their own Czech/Bohemian Catholicism. And yes, while religion is far less of a political consideration in the 70s, than it was in the 20s, it's still one of many tools to be wielded. And the revived religious orders might come into play here as well.
Of course, in the end it will not be clear cut, but a mix of elements and things that I very likely missed, but this should give some ideas at least.
Now then we have Michael. I get the feeling he's mostly the military men, a figurehead in many respects. Still, he has some of his own ideas. However I very much get the idea that despite everything he isn't representative at all for the average Czech who's king he is. And the handful of Czechs we see all seem to be pretty German-assimilated military men (unless I missed something).
I actually forgot if he converted. I think I remember something about that (when there was discussion of Kiki staying IIRC with the Russian-Orthodox church quite a while ago) but I could be wrong. He certainly acts like it for some parts. As mentioned he's talking to the Pope, so those are explicitly catholic order that he is trying to revive (though I hope they take more the current charitable form, not the meritorious order that IIRC the Johanniter were in Prussia). He's got cavalry and chivalry nostalgia, I can tell. I wouldn't be surprised if people tried to relate him to Maximilian I. "The last knight". (Though his centre of power was Tyrol, not Bohemia...)
When it concerns Alberta, I'd assume we have a conflux of a Hohenzoller family that very much tries to spread themselves broadly over the Confessions, leaving a lot of it up to the individual, and a reluctance from the English side to loose their grip on a girl that is still pretty high up in the line of succession. If she were to convert, she might even conspire with her sister-in-law who had in turn married the the heir of the Jacobite Pretender!
(And I seem to be in the mood to write up long posts, uselessly speculating... oh well)