Whereas I'm rather hoping they'll split into hundreds of different sects over how many Angels can balance on the tip of a needle or something like that.
The religious policy of the state will be a free religious market with free competition and zero public funding.
In practice that means don't preach "bloodline", anti-gay or pro slavery nonsense, get your followers to donate freely and don't get too big and you should do fine. Whether you're the reformed church of Xthonos, church of the latter-day Angels, a branch of the Hallasurq faith, the divine druids of the forgotten Gods, or the temple of the holy and fearsome spaghetti monster.
The revolutionary state really wouldn't care all that much about religion so long as it steers clear of those taboo topics and the individual churches/denominations don't grow too big.
Currently under the Karagond Codex I believe dynasties among the upper-classes operate along more Roman lines where the family name, not the bloodline of the child is considered the most important and adoption and gay marriage are fully allowed.
The bloodline nonsense is a possible drawback of the Shayardene Codex (since the Laconnier conspiracy is likely based on that one). At least that 's what I read between the lines and it would be another and altogether different reason why the Shayardene Codex might be anti-gay in practice, even if isn't in theory, depending on how much the bloodline nonsense is prioritized.
The slavery and caste system issues are rather obvious, they're the foremost thing my mc is fighting against and any priests who'd endorse slavery, no matter what Codex they use, are full-blown counterrevolutionaries, period!
It's why my INT focused mc aims at splintering the church into insignificant little pieces and wants to introduce a religious "free market".
That's what the blood tax would be for ideally, perhaps blood isn't even needed at all, maybe the essence of magic can be obtained some other way. The unbelievable amounts of fear and dread while being Harrowed apparently do something to make blood more potent, but in no way is it certain those are the only feelings/emotions that work. Maybe a lovefest right before the blood tax could work just as well if a (slightly) different extraction/distillation process is used.
The mc's live arterial blood certainly works well-enough in most cases, although it is horrifically limited in quantity.
Since those undead can apparently use magic and likely lack blood my mc would be most curious as to how they manage to do that and if that process can somehow be substituted for the current Harrowings. In any case Gaesh the arch-lich certainly seems to predate the Hegemony by a fair bit of time.