Alternatively, follow the pre-Christian Ancient Roman approach and maintain unity by assimilating foreign religious practices. I think polytheism makes this method easier.

Christianity has assimilated other religions and their practices, though.

As a prime example, many elements of Christmas such as the yule log originate from so-called pagan religions such as Norse.

> Christianity has assimilated other religions and their practices, though.

And over the years Christians have persecuted many when their beliefs didn't agree with the dominant interpretation. The Romans were relatively tolerant of indigenous beliefs, as long as they didn't lead to rebellion.

At certain points in its history, Christianity was fairly eager to ingest aspects of existing religions if it meant that they got the account (conversion). This eventually became controversial (eg see https://en.wikipedia.org/wiki/Chinese_Rites_controversy), but a lot of early regional Christian saints, say, are, well, suspiciously similar to pre-existing deities or other pagan figures.