Being a Christian was a crime in the Roman Empire in the first 300 years of Christianity. However, as Justin Martyr, Tertullian and others have pointed out, there was a vast inconsistency in the way the Romans treated the Christian "criminals" compared to how they treated the murderers and thieves.
When a thief was suspected of a crime, they would arrest him and sometimes torture him to get the truth out of him. It was actually the opposite with Christians: A Christian would already self-identify as Christian and then the Roman authorities would use torture, prison or gladiator spectacles to get the Christian to deny it.
This would be a good time to pause and ask--What benefit did it serve the Romans to do this?
It is not like the Romans were trying to do them a favor by going through all this torture to make the Christians honor the pagan gods to spare them from death. That would have been just too generous. Why did the Romans go through all the trouble to torture admitted believers into denying what they had already publicly and proudly affirmed?
It was about domination. It was a fight for the soul of the Empire. It had nothing to do with justice. If simply being Christian was a crime, then certainly the verdict should be easy if the suspect was fully admitting it. If an admitted believer denied their Christianity in the face of torture, it was not like anyone was going to believe that "confession." In fact, there is evidence that the Romans (as well as the Christians) shunned the people who caved in.
The goal was to see if Roman might was able to break the spirit of a believer. They could return that person tattered and broken back to society, somehow "proving" that the Roman Empire had the ability to conquer dissidents. In this macho, honor & shame society, this was a big deal. Was strength and force enough? The Christians answered: No!
The Romans even stopped torturing women on some occasions, because when the women endured the torture and held their heads up high and continued to affirm their Christianity even to the point of death under the most terrible conditions, it was a absolute shame on the Romans. Consider the language: They felt "conquered" by these women! Now, can can someone who tortures someone to death be the one who is conquered? There are certainly deeper theological reasons as we have seen in the passion and death of Jesus himself. Jesus promised us that might does not make right, and that military and political force do not have the last word.
Roman power was not able to win. They could not intimidate, force or manipulate people to follow their will or make happen what they wanted to make happen.