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I can answer with regard to early, ante-Nicene Christianity, principally through the second century, with some peeks into the third and fourth. There are several parts to this answer.

TL;DR: The short version of this is that syncretism usually worked locally, only after military conquest of a new people in a single place; that through the early centuries, Romans did not see Christians as a people to be reckoned with but a troublesome sliver of a minority which acted seditiously; and that while there are examples of syncretism, they existed according to their mental framework about what they thought Christians even were. However, more important than syncretism would be the difficulty of reconciling Christian claims into the Roman mindset. Among these were the former Christian Celsus' attempt at a philosophical refutation of Christianity and what became called, by the Great Church tradition, heresies. By the time Christians were a large enough population to care about, they were largely not considered disruptive to social order.

First, when Romans did incorporate gods into their pantheon, it was principally by creating a narrative that suited a small, local cult in order to help assimilate a conquered people into the Empire. Romans were generous conquerors in matters of religion. You didn't have to renounce your local gods, so long as you accepted Roman worship as well, when necessary. Religion was largely governed by a matter-of-fact pragmatism. Why would you insist that someone else's god wasn't real? There are gods everywhere, in the city, in the fields, in the home. Maybe there are different gods in this new region. It is characteristic of ancient Mediterranean religion that whenever you are in a place, you should follow local customs, even if you visited Egypt and their weird, primitive, but assuredly ancient animal gods. You don't have to like it, but it doesn't hurt to be polite. To be ancient in the ancient world earned you certain privileges---afforded, by the by, to wealthy Egypt and the austere Jewish (proto-)diaspora alike. "When in Rome, do as the Romans do" is pretty expressive of this attitude. Besides, if you were educated, you were much more interested in the Platonic hope that you might achieve union with The One sometime in your life---the pantheon was popular window-dressing to be rationalized, when possible, into your Platonic commitments. The long and short of it is that local gods were not universally syncretized in any practical way. They were pragmatically syncretized. Functionally, it is where you were at the time that determined which gods you would worship, and it was the location of temples and places of worship which determined which ritual you would undergo. At best, the god of a conquered people would be locally married off to an equivalent god or goddess of the Roman pantheon. Christians were not a conquered people, so the typical apparatus was not invoked.

A second thing to understand is that the approach to religion around the Mediterranean was tied very closely to political and social activity. On the city-wide level, this meant the (frequent!) religious festivals were the fabric of the social life. You see a parade, you get a hunk of meat---usually pork---you cheer in large crowds. It's fun! Why wouldn't you want to do this? Christians absented themselves---and unlike Jews, they were not ancient, so they were not exempt from such rituals---which made them suspicious. What kind of person would go to the University of Alabama and not shout "Roll Tide?" Maybe ... they're rooting for Tennessee, which would clearly be equivalent to desiring the destruction of the Empire. Coupled with the fact that originally Christians were still a tiny minority religion, educated Roman administrators were more concerned not with the incorporation of Jesus as a figure into their pantheon but with how to deal with these Christians who were being accused by their neighbors of impiety. What do they do? Ante-Nicene Christians were accused of everything from simple impiety to incest and ritual cannibalism---cover an infant with flour, have the Christian novice beat the flour until the infant is dead, and have him chow down, unawares.

When Christians were met with less hostility, they were originally characterized as one of two sorts of groups: a philosophical school, in the model of the itinerant teachers for hire---"I know what they are. They're like those wandering Platonists who take money for teaching"---or, more dangerously, a burial society. Remember when I said that religion of some kind was the fabric of society, which existed in large, public spectacles? This was true also on the micro scale. Small groups, under the banner of a common divine patron, banded together for mutual support---remember the Roman Empire did not have institutional welfare. To provide for their loved ones, people joined these burial societies. They had rituals and devotions, but were largely small social clubs which guaranteed that they would take care of things when you die, especially burial expenses, so long as you put up a membership fee to start with, which in part paid for a big feast for all current members. These groups fell in and out of favor by the government for reasons of political stability. If you are administering an empire, do you really want lots of small, secretive, potentially seditious groups? (For more on this, read the Wilken below. I wish I still had a copy! It's a very easy read, transformative.)