They were "persecuted", just not for no reason.
Early christian tradition included:
- defacing statues of the Gods
- storming temples of the Gods as groups, sometimes attacking priests
- burning pagan books, including scientific or artistic ones
- defacing "pagan" (all) art
- sitting on pillars and not coming down, even to shit (google it)
- yelling blasphemies about the Gods in public Forums, and overall making a fuss
- preaching their "religion" with enough loudness and disrespectful attitude to make modern evangelicals blush
- completely dismissing political nuances like respecting authorities
- being extremely dirty to make a point against "vanity"
- not being productive for society at all, because that's profane, worldly stuff, man
They were basically a gang of vandals.
If a group came and did the same thing to christians today, we'd have people calling for their death penalty too.
Oh, and most killing of christians wasn't done "officially", by cohorts ordered by Rome. It was done via mob violence, when the locals got sick of their shit.