That’s a really difficult question to answer for a few reasons. First, there’s no such thing as “Christians” in the first century. We have no attestation of the word until the 80s or so, and the two references to it in the New Testament (Acts 11:26 and 1 Peter 4:16) imply that it was an outsider designation and, possibly, derogatory. Second, even once “Christian” becomes a category that a person can claim belonging in, recent scholarship is finding more and more reason to think that it wasn’t always a primary identity, and it wasn't a unified one. Not everyone who might have called themselves Christian necessarily felt like they had anything else in common with other Christians. Like I’m American and so is Rand Paul, but that doesn’t mean we jive on every topic or have the same understanding of what it means to be American. The identity “Christian” certainly wasn’t mutually exclusive with other identities, like “Roman.” Third, the scholarship on identity and especially orientation toward the Roman empire in this period is still pretty young.

Also, just like the term “Christian,” the term “Roman empire” has a lot of modern assumptions and hindsight behind it that ancient people didn’t necessarily share, one aspect of which is ideological unity. People in the farther eastern provinces would probably have experienced Roman power very differently than people in Italy or even Greece, and people in Ephesus would have had a fundamentally different experience of Rome than people in Jerusalem. Many people in the empire would never have considered thinking of themselves as not Roman, no matter how they experienced it, and many others didn’t think of themselves as Roman at all even if they were very privileged. As groups, Christians and Romans were less unified than we tend to assume.

We can look at some early Jesus writings and, with some historical contextualization, come to some conclusions about the ways that their authors experienced Roman power and what they thought of it. The Gospel of Mark, for example, is widely thought to have been written soon after the destruction of the Jerusalem temple. Working from there, and with some background knowledge about the First Roman/Judean War, we can look at the ways that the text talks about power, kingship, military issues, etc. There is a lot of ambivalence about royalty in that text--Jesus sometimes accepts royal titles, and sometimes rejects them, and sometimes transforms them (Son of God is a Roman imperial title, and Jesus turns it into the Jewish apocalyptic reference Son of Man). The crucifixion is full of ironic royal imagery, like the crown of thorns. Rome is also portrayed very ambivalently. The idea that Pilate just passively and even virtuously returns the decision to crucify back to Judeans misses the fact that he’s very skillfully undercutting the power of the Jerusalem aristocracy, who also doesn’t come out well in Mark’s portrayal. Judean politics in the first century were a mess, which is pretty well reflected in Mark.

On the other hand, you have someone like Paul, who says in Romans 13 that people should obey the authorities and consider them part of the divine ordering of the universe. Paul is coming from a very different place than Mark. For one thing, Paul is writing before the war, so he doesn’t know that Titus is going to destroy the temple. For another thing, Paul is addressing people who seem to be, for the most part, functioning members of Roman and Greek society. Human social structures as part of the diving ordering of the universe is a basic principle of all ancient Mediterranean cultures that I know of, so Paul isn’t telling those people anything that doesn’t fit with things they already take for granted. Mark is writing to people who just witnessed (and maybe participated in and lost) a war. Paul’s addressees are dealing with “first-world problems,” comparatively. Questions about obedience to authority probably have more to do with whether and how Jesus worship allows participation in civic culture, including questions of slavery, than majorly anti-Roman sentiment.

By the early second century we’re seeing Christianity as a category, and probably one that is self-claimed. That’s also when we get our earliest preserved Roman portrayals of Christians, and those aren’t good. Based on the evidence we have, elite Romans saw Christianity as a dangerous movement, not necessarily for any material political resistance, but because they were abandoning The Way Things Are Done, which was cosmically important in the ancient world. Following ancestral traditions, like the Jews did, was a justifiable reason not to participate in a lot of Roman ones, but most Christians weren’t Jews, they were Greeks and Romans who were abandoning ancestral traditions--an entirely different and dangerous thing. Reading between the lines of Pliny the Younger’s famous letter to Trajan (10.98), persecution of people simply for being Christian was known though not necessarily widespread by the second decade of the second century. The letters of Ignatius corroborate that, although it’s sometimes difficult to tell whether the earliest martyrs would have had any problems if they hadn’t been in positions of leadership. Nobody seems to be stopping Ignatius from writing his letters from custody, or, as far as we know, arresting their recipients. It brings up the good question about what charges were actually being brought against people like Ignatius and Paul.

So we can see how Christians in the second century could be feeling the threat of persecution even if it wasn’t immediate. But we can’t really use that as evidence to talk about their feelings toward “Rome.” Lots of people feel threatened by their governments without disavowing their nationality. On the extreme end we definitely see demonization of Rome--that’s what most of the book of Revelation is. Less extreme, we see writers like Justin Martyr arguing for Christianity as a separate ethnicity from Romanness, but not necessarily with the same ire as in Revelation. Later, of course, as more and more elites joined up, Romanness begins to become equated to Christianity, but more often in the earliest writings there’s a lot of ambivalence that I think is less about being “pro” or “anti” Rome and more about exploring what it meant to be Roman or to interact with Rome/Romans AND what it meant to worship Jesus/be Christian within contemporary social structures.

Paul never uses the words "Christian" or "Christianity." He says "in Christ," most of the time, and addresses his letters to "ekklesiai," which is a very generic word in Greek and is better translated "assembly" or "gathering" than "church." The book of Acts uses "the Way," and the one time the word "Christian" appears, it's written in such a way that it sounds like outsiders are calling them that, rather than an insider term.

There were certainly people who worshipped Jesus and who understand themselves to have things in common with other people who worshipped Jesus. But recent scholarship is finding that using words like "Christian" and "church" can lead to a lot of bad assumptions, because we think we know what those words mean. Calling Paul Christian puts him in a category that carries a lot of assumptions with it, so there are questions we don't ask because the word "Christian" answers them. But if we recognize that Paul had never heard that word, that he was in the very beginning stages of what that word would come to mean, there are a lot more questions to ask.

I would say that even the assumption that early Jesus folk thought of themselves as Jews is really limiting, because while it's probably true for many of them, it wasn't for many others. Also, we have the same problem with "Jew" as we do with "Christian," which is that it's taken on a lot of meanings in the past 2000 years that may or may not be helpful for this period, in terms of understanding ideology and culture.