No!!!
Why does the Crown need to pretend not to know whether gods are real? Obviously gods are real! Who else would be doing the miracles?? Ms. Wójcicka didn't think they were real, but that's because — well, it might not be because she's stupid, if she's really never met a real priest or seen any magic and she doesn't trust priests who can't do magic to be telling the truth. But even if miracles and real priests aren't very common, the Crown should still know. It... might be harder to know for sure which gods are really powerful, if some of the 'saints' are a lot more powerful than others (or not even really saints at all), or if there are lots of gods that are hiding like the Asmodeans might have been... but it still seems like they should definitely be able to know some of them are real. And obviously if they didn't know it would be important for them to find out, so that they'll know which ones are worth praying to and which ones are really just... faeries, or regular dead people with no special powers.
...Also, she doesn't see why the Crown wouldn't just put out books talking about the three gods that are really popular and saying that Jesus Christ supports the president and that sort of thing. It doesn't seem like there are a lot of people here who are against the Church. Maybe there are, and they just aren't as common around here, or maybe there are a lot of people like Ms. Wójcicka, and they'd be upset if the government were telling people about the gods because... they think governments... shouldn't tell people to obey the gods rather than following their conscience? Shouldn't lie? Because they think the Church's rules are bad? None of those really make sense, obviously governments are going to tell people to obey the law, and lie to them sometimes, and promote the gods that they think are good for the Crown.
When she was talking with the guardsmen a lot earlier, some of them mentioned that there was an Orthodox and a Jewish and a Muslim god too, though it sounded like the Orthodox and Jewish gods might be the same as the Church's gods. (Also something about the ancient Greeks, but presumably those aren't relevant anymore, if they're ancient?) Maybe in this part of the country there are a lot of people from the Church, and in other parts of the country there are Muslims, and the president wants them both to support him? Except in that case the 'libraries' in this part of the country could just talk about how the Church supports the president, and the libraries in the other parts of the country could talk about how the Muslim god supports the president.
"...Not really. I don't see why people would... want the Crown to pretend like they don't know anything about the gods? And I don't see why the Crown would want to pretend that, rather than just lending people books about how God supports the president."
(...Maybe the Church's gods don't support the president, and the president knows it, and that's why the priests here mostly can't do magic, because the real priests were all executed? And he's worried that if he says in the library books that the gods support him, they'll do a miracle to tell people he doesn't? Except it doesn't really seem like putting it in the library books specifically would make a difference.)