In his last book, 'The triumph of Christianity' Bart Ehrman writes about this: “ I need to stress that organized opposition to the Christians came, for the most part, in isolated incidents. The church did not experience perennial violent persecution. The idea that Christianity was an illegal religion under constant surveillance by a state apparatus that inflicted martyrdom on many thousands of believers, forcing the church underground into the Roman catacombs—all this is more the stuff of Hollywood than of history. Christianity was not declared illegal in the empire before the middle of the third century. There were no empire-wide laws or decrees issued by the central authorities in Rome that proscribed the faith. Christians did not, as a rule, go into hiding. For the most part they lived perfectly normal lives in the midst of other people who practiced a wide variety of other religions. The catacombs were not meeting places for Christians forced to congregate in clandestine cells for fear of violent persecution. Persecution itself was rare, and there were relatively few casualties.

But it did happen on occasion, and there were indeed some ghastly incidents involving trials, tortures, and horrific executions.”

So, yeah, for the most part Roman authorities just didn't care about that and even when they did (for example, Diocletian, 303): "“It was one thing, however, for Roman officials, even emperors, to issue an edict and another thing to enforce it. No imperial police force existed to carry out the requirements of Diocletian’s decree. Enforcement was a regional or even municipal affair. Apart from a few church building destructions, the decree had little effect in the western part of the empire, and enforcement in the East was spotty. Still, those could be very hot spots indeed.”