Ironically, it's probably rebelling against the gods of this universe that is Syla's crime. Indra calls her an apostate and a recusant. An apostate is someone who breaks from their faith, while a recusant is publicly vocal about their dissent from accepted doctrine. We also know that Valravn sees Syla as a friend and doesn't understand why she isn't joining him in his service to the Lord of the Dark. The Lord of the Dark sees the Apostles as parasites and aims to sever their connection to the universe. Put it together, and I'd say that Syla was preaching a similar heresy to the Lord of the Dark's position. That the Apostles aren't gods, and don't deserve their worship and reverrence. That fits with Indra hunting her, we know from the Asura's profile page that punishing heresy is a job Indra has been given before.
qrd
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God (true, Divine Creator) is real, worshipped by both mankind (fell out of fashion, but there was still the huge church where Tiffany was to be wed, plus the nun during Nico's sex scene) and elder beings.
The Asura were a mighty race of monsters who worshipped God, too, and saw the apostles (personified dae --> daemon) as heretics for wanting to be worshipped as Him. The apostles threw a fit and gave Indra their blessing to enslave/kill them all. This is presumably the fate of all significantly powerful monsters who refuse to obey them. I suspect Syla was ordered to be executed because she, the Chosen and leader of the most powerful Mind species, wanted to spend the next 70+ years as MC's mom.
Edit: After reviewing Syla's flashback and final action, this is definitely true because she cried "You'll kill [all of the other Chosen]!" and made Indra forget their identities. The current Chosen would be on Indra's hit list because they either don't care about the Apostles and duty (ex.: Eisheth Zenunim, Rebis) or recognize that they aren't God (ex.: Aglaecwif, Valravn).
I'm hesitant to trust the Lord of Dark because of the past valkyrie/merman alliance war against him. My guess is that the 7th Apostle and Valravn plan to cover the world in darkness so that he can repel all other "false gods".