The discussion of how a still Republican Rome would treat Christianity has been thrown around on occasion. Certainly room for more latitude, and more variation in treatment.
Regardless, lets flash forward a few centuries. The Republican forms are still going strong, and the population is becoming predominantly Christian. Giwever, the Senate and the still relevant positions of Pontifex Maximus, Censor, and other such religious political offices don't really mesh with the new religion. How might the government cope?
To clarify, this is more a discussion with how the Republic deals with a dwindling number of men that can be Pontifex Maximus, how they deal with citizen assemblies that refuse to acknowledge the traditional auspices, that sort of thing.