(note: Some of this information is taken from the remastered Player’s Guide, if anything seems inconsistent with that document consider what’s written here to be overruling)
Being under Thrune rule worship of other gods is somewhat permitted in Kintargo. By the letter of the law the people are allowed to worship other gods only if they worship Asmodeus first, and above all others. That being said those gods whose doctrines and causes clash with the strict, oppressive hierarchies of the Infernal faith are often decried as heresy by Asmodean Inquisitors, and open displays of their worship can very much see you imprisoned, or just as often publicly executed.
Despite this people don’t just give up on their beliefs, and when the guards aren’t looking people will still invoke the names of other gods, or have private shrines in homes or places where they gather in secret. You can assume it’s fine for your character to worship another god, but they likely wouldn’t have gone around bragging about it to the city guard.
Major Deities
Tolerated faiths with a presence in Kintargo
Deities who command their followers to obey/respect the law are usually treated with some extent of tolerance by the Thrune regime, as their faithful tend to begrudgingly accept that the worship of Asmodeus is simply the law of the land in Cheliax.
Shelyn
As the patron goddess of art and artists Shelyn has probably the most substantial presence in Kintargo. Given that the goddess commands to be peaceful and try to see the good in all people, Shelynites aren’t commonly, openly rebellious. That said, the Asmodean faith still regards the cult of Shelyn with suspicion, and with Barzillai Thrune’s arrival all of their ceremonies and gatherings are supervised by either a Hellknight or Asmodean priest.
Abadar
Likely one of the most openly tolerated, Abadar is often said to be a tense but constant ally of Asmodeus, owing to his respect for the law and civilization. It also helps that the temple-vaults of Abadar hold most of the wealth of Cheliax’s upper class. That said, not all Abadarians are willing collaborators, and many resent the Asmodean clerics and their propensity to abuse the law to gain power over others.
Pharasma
Owing to Pharasma staunch position of impartiality, and the role of the Hells in the cycle of sould, Pharasmins tend to not interfere in Chelaxian politics at all. As long as nobody is raising the dead or interfering with the cycle of souls they simply see no reason to. As a result the cults of Pharasma are left largely alone to go about their business, though recently Barzillai Thrune has mandated all burial ceremonies now be overseen by a priest of Asmodeus.
Iomedae
Relations between the Iomedaens and Amsodeans are tense. Being the inheritor of Aroden, god of humanity and former patron-god of Cheliax, Iomedae’s faithful have a substantial presence across the empire. And Iomedae’s faith has always emphasized a respect for law and justice, even if it impugns on personal freedoms. The more cynical Iomedaens have accepted the Infernal faith as a necessary evil to uphold the law, the more idealistic ones deeply resent what they view as a perversion of the ideals of justice and lawfulness. But as the campaign opens rumors come in of Iomedaen zealots having started their own rebellion in the south, and many of her faithful in Kintargo are keeping a low profile for fear of reprisal.
Torag
Like Iomedae the worship of the dwarven ancestor gods emphasises lawfulness and justice, and so tends to begrudgingly accept Asmodeus dominance in Cheliax. Despite this Torag doesn’t have a big presence, as there aren’t many dwarves in Kintargo.
Erastil
Erastil commands his faithful to keep the peace and take care of their homes, and as result is not seen as opposed to Asmodean primacy. Erastil has a respectable presence in Ravounel’s countryside, less so in Kintargo proper.
Irori
While tolerated Irori has little to no presence in Kintargo, his most visible followers having been the Sacred Order of Archivists, which has all but disappeared and was considered heretical by the church of Asmodeus.
Nethys
Nethys is not popular in Kintargo, aside from the odd student at the Alabaster academy. But being a very disinterested and impartial god his worship is somewhat tolerated, just as long as his faithful don’t use their magic to break the laws.
Zon-Kuthon
Due to Cheliax’s alliance with Nidal, worship of Zon-Kuthon is allowed and practiced in Kintargo, though generally not by anyone except the few Nidalese who live there. Most of Kintargo’s citizenry has no love for the Midnight Lord, but few will openly discuss it for fear of attracting unwanted attention.
Faiths with presence in Kintargo, considered Heretical
These dieties have had their shrines burned, their temples confiscated, and their worship is outlawed and mostly practiced in secret in and around Kintargo.
Milani
Though considered a minor Goddess, Milani was once a saint of Aroden’s faith, and had a huge presence in Kintargo. Being pretty much diametrically opposed to the Asmodean faith the cults of Milani have been constantly hounded by the inquisition. Of the once-many cults of Milani, only one, The Rose of Kintargo, remained for the longest time. Though rumor has it that Barzillai Thrune has recently eradicated the remnants of this cult as well.
Cayden Cailean
The church of Cayden was burned down during the civil war, and never rebuilt. Instead the ground was given to the followers of Zon-Kuthon. Caydenites have been in hiding ever since. Many of the cities taverns and gambling halls have secret shrines to the Drunken Hero, and rumor has it the former mayor may have been a worshipper.
Desna
Asmodeans absolutely despise Desna, if only because her faith being so tied to nomadic lifestyles means there is no central place of worship for them to round people up in and burn down. While her faith is strongest in Ravounel’s countryside there are still secret worshippers within Kintargo.
Calistria
Originally Calistria had a big temple-brothel in the city called the House of Satin Veils. After the rise of House Thrune the temple was confiscated and given to the Abadarians, who renamed it the House of Golden Veils. Calistria is worshipped in secret, but is still very popular with the citizenry, especially sex workers, and some of the more devout followers deeply resent the church of Abadar for occupying their former temple. Most, though, reserve their hatred for the Thrunes, but lacking any kind of organization or leadership, have never done anything about it.
Sarenrae
The Everlight never had a big presence in Kintargo, most of her followers being recently converted by the popular bard Shensen, who used the Opera house as a central place of worhsip, but who has not been seen or heard from in a while.
Faiths with little to no presence, considered heretical
Norgorber
There are no known cults of Norgorber in Kintargo, but that is exactly as Norgorber commands so… Either way the church of Asmodeus does not like the masked god, nor his followers.
Gozreh
Gozreh has very little presence in Kintargo aside from the harbor, where sailors sometimes pray or curse their name in equal measure. EIther way the church of Asmodeus considers them a harbinger of chaos and disruption, and worship is explicitly forbidden.
Gorum
Note: at the time of this campaign Gorum is still alive Gorum basically has no presence in Kintargo, and the church of Asmodeus likes to keep it that way.
Lamasthu
Worship of Lamasthu is explicitly forbidden and looked at with disgust by both the church of Asmodeus and the general citizenry. Aside from the odd Goblin running his mouth nobody openly talks about the Mother of Monsters in Kintargo.
Urgathoa
Similar to Lamasthu. With the added bonus that rumors of Urgathoan worship is one of the very few things that will move the chruch of Pharasma to action, with extreme prejudice, at that. Though many of the poorer citizens like to imagine some of the nobles might be secret worshippers nobody talks about Urgathoa.
Arazni
(At the time of this campaign, Arazni is not yet ascended and is stuck in 1E edgelord writer hell. And also Geb, the country, not the guy.)
Worship of other entities
Worship of any of the Archdevils, Infernal Dukes, Malebranches etc. is allowed, and encouraged in Cheliax, though people will still be reminded Asmodeus rules over all.
Worship of Empyreal lords (Angels, Azata etc.) is mostly forbidden, though perhaps tolerated if the entity in question preaches obedience to the law. Exception to this is the cult of Ragathiel, which is banned by the church of Asmodeus, as the redeemed angel is considered a heretic and traitor to the Hells.
Worship of Demons, Daemons, Outer Gods, and chaotic entities like Proteans is fairly rare, but also highly illegal and liable to get Infernal Inquisitors sent after you.
For most other deities and entities one can consider their worship tolerated as long as they preach obedience and/or submission to the law, and to not cause trouble. Entities that align themselves with Hope, Freedom, or just Chaos are generally considered heretical by the Asmodean faith.