Established in Canon Traveller are:
+ The Vagr Church where Vagr believe they are the choosen tool of the Ancients and that said Ancients will come and finish their work any day now
+ The Iilish church that believes only dying on Iilish guarantees you passage to the afterlive and that pacifism is the way. Guys prefer black and a certain Archduke (while not a believer) honors them by doing so too. The church later adds "dying in battle for the domain" as an alternate way to the afterlife but does split over it.
+ The KKree with the "kill/subject all meat-eaters"
+ A number of planets have religious dictatorships (including one base merc ticket)
+ The Vilanie have priests/food chemists and prayed to ancient maschine gods (Ancient Artifacts) during their early days
If/what religions still exist will depend on the region of space and the politics of the individual religion.
I'd assume the Solomanies to repress Religion since they believe the Solomanie Movement is the end all and be all. OTOH that could result in some nice adventures, smuggling members of religious groups over the border, rescuing them from prison camps etc. Time to dust of the "Missing in Action" video tapes
The 3I will allow/ignore local religions unless they are interfering with trade. So an extremly isolationist movement on a central planet (Say major trade-route crosspoint) will get the attention of Imperial Intelligence. Most likely a long term project designed to split the religion in multiple sects.
The 3I will keep an eye on religions advancing past a single world and/or affecting a higher nobel. Can't have a duke go pacifist and drop defence-readiness, can we. What do you mean, the duke fell out of an airlock? Bad accident, send our regrets...
I'd say Zhodanie will have no religion, it seems not right for them. More a "think right" philosophy encouraged by the Thought Police.
The Hivers most likely teach "Inventing local Religion for fun and profit" as part of the Bachelor of Manipulation. Did anyone realise that the great old ones tend to have lots of tentacles...