The Romulan Star Empire could well have been like the Roman Empire. Using Shinzon and Sela as examples; a non Romulan can advance in the system. Those non Romulans advancing have to work twice as hard to get half as far. Nothing new about that.
In ancient Rome a non-Roman can be a citizen and have all the rights as a Roman. The same seems to hold true for the RSE. This would not be through enlightenment but pragmatism.
As for religion, if the Praetor of the moment doesn't see it as a threat to power, they'd be indifferent to it. The RSE probably would not worry about any Earth based religion. The Surakians, led by Spock is another matter.
Rome had its periods of enlightened rulers like Marcus Aurelius. The RSE probably has the same. Then there were the types like Caligula. Who'd want to imagine any type of Romulan equivalent to that?
Like other posters have written, the Romulans like the Romans would probably have positive influences on their tributary or subject worlds. There was a TNG novel written several years ago in which a world had to choose between allying with the RSE or the Federation. I forget the title, but the conclusion is not a foregone one.