So as is often lamented by scholars of Roman history, we know very little about Slaves in the Empire, relative to Patricians. However, it is clear that Christianity was immensely popular with slaves which made up a good portion of the population. The slave population acted as a conduit for converting significant portions of the Roman citizenry over time, well before Constantine became Emperor.
If we know so little about slaves in the empire, then what is the basis for such specific claims about them? Also, what was the proportion of slaves in the Roman empire? The highest estimate I've seen is 15%, so even if 100% of them at that time were Christians, that's still a minority religion and still pretty close to the estimate I gave of 10% at most prior to the ascension of Constantine, but what evidence is there that literally 100% of slaves were Christian? Surely the unquantified claim of it being "immensely popular" among slaves isn't evidence for that; after all, if 50% (so 7.5% of the population at highest estimate) were Christian, it could be said that it was "immensely popular". Likewise, if it was a third (5%), a quarter (3.75%), or even a fifth (3%) of the slave population, it could still claim "immense popularity" among slaves, because the term "immensely popular" is relative and conditional. As to your last point here, the contention isn't that slaves had no role in spreading Christianity, it's that prior to the crisis of the third century the evidence we have indicates an insignificant Christian presence in the empire, and prior to the ascension of Constantine it had risen to at most 10%; not socially invisible anymore, but certainly a small, minor religion. It can simultaneously be true that slaves were a conduit for what conversion did happen prior to Constantine and his successors, and that Christianity amounted to only minor penetration of the Roman empire prior to Constantine.
Constantine's most cynical critics state that the only reason he made Christianity the state religion was because much of the power base was rapidly converting to Christianity...not some miracle he witnessed. It’s hard to believe that such a political and military mastermind would make such a weighty decision for the sake of 10% of the population.
I’m pretty sure Constantine also banned gladiatorial games due to the blood sport being incompatible with Christianity. Doesn’t seem like a wise move if only 10% of the population agrees.
As a final point, he did this with relatively little pushback.
To the first point, Constantine didn't make Christianity the state religion. He did, however, publicly favor Christianity and denounce paganism from the very beginning, financially support the Christian church, and sporadically close and even plunder pagan temples. He may even have banned public sacrifices at times, though there's some controversy over that in the scholarship. Were these relatively mild things? Yes, but they would have made clear that the imperial office, the highest in the land, favored Christianity and was hostile to non-Christians, which would drive conversion. This would only become rapidly more extreme as Constantine's successors would take the throne. Also, there's zero reason to suspect Constantine wasn't a sincere Christian, which means there doesn't need to be some political reason for him to convert - though there's no shortage of explanations for why he was a Christian, and it doesn't need to boil down to legends about a dream or miracle that he witnessed. His mother was a devout Christian, mind. At the end of the day, though, the question of why Constantine was a Christian or the sincerity of his Christian faith are neither important nor useful because it's all speculation and can't be used as evidence for Christian numbers.
As far as banning gladiatorial games, you do realize that they were controversial even among pagans, right? And finally, for him receiving relatively little pushback, I don't think you quite understand the position that Roman politics was in when Constantine took the throne. For decades, the Roman empire had been destabilizing and Roman emperors had been consolidating power in the imperial office as well as becoming increasingly despotic and iron-handed. By the time Constantine took power, the emperorship looked more like a military dictatorship and the civil governance was in tatters. That Constantine got away with this or that says something about the increasing centralization of imperial power and nothing about Christian numbers.
Jews were successful in Ethiopia and Yemen, Yemeni Jews still exist today and are likely one of the key influences for Mohammed's life
Okay then, what is the context behind the success of Judaism in Ethiopia and Yemen? Was it "bottom-up" or "top-down"? How thorough was it? Did an entire sovereign group "judaize"?
Christianity was popular in the East and some of the west. The east had far more population centres as well as more integrated trade routes and social mobility, and not to mention being close to Jerusalem. Yes Gaul and Brittania weren't very Christian at the time of Constantine's acclamation, but Christianity was of growing significance within the empire, and as always, if the influential believe it its irrelevant to what the majority believe.
That Christianity was more popular in the east than in the west doesn't negate the premise that it was insignificant prior to the crisis of the third century. Both can be true at the same time. I actually did state that Christianity was of growing significance within the empire at the ascension of Constantine, hence "essentially microscopic until around the middle of the third century... around 10% of the empire's population at the ascension of Constantine." Notice how they went from "essentially microscopic (insignificant)" to "10% (of minor significance)"? My contention is that there is zero reason to assume it would have become the majority religion of the empire (and no reason to assume it couldn't possibly have slipped back into irrelevancy later on) had Constantine and his successors not wielded state power to its benefit; rather, that Christians had gained control of the imperial state is precisely the reason it became the majority, and eventually sole, religious paradigm of the empire.