That's not true. Roman citizenship was sacrosant, there was even a war during the late Roman Republic time between the Romans and allied Italians https://en.wikipedia.org/wiki/Social_War_(91%E2%80%9387_BC) fought over it. During the Roman Empire, Caracalla extended citizenship to everyone mainly to spite the Senate.
I think there is no denying that religion was important in Rome. However what I can gather the Military was more important for citizenship and status.
Military service was one of the main ways to upgrade your social status.
For non-citizens, the reward of Roman citizenship after 25 years' military service offered social transformation, not only for themselves, but their families too.
The Roman empire was large and diffuse enough, and enough people had local power that it was becoming increasingly difficult for Romans to hold power by force alone. At some point, you need _just enough_ people who feel like they have a stake in "the system" that they participate in supporting it rather than tearing it down.
The following two articles barely mention religious status.
https://en.wikipedia.org/wiki/Roman_citizenship
https://en.wikipedia.org/wiki/Social_class_in_ancient_Rome
I think there is no denying that religion was important in Rome. However what I can gather the Military was more important for citizenship and status.
Military service was one of the main ways to upgrade your social status.
https://www.britishmuseum.org/blog/introduction-legion-life-...