According to the Romans, Jesus was a nobody. The Romans had a very contentious relationship with the Jews of the period, but generally respected the Jewish faith as an ancient and decorous religion. As such, when Jewish communities by-and-large condemned new Christian cults as a bunch of troublemakers spreading nonsense, Roman authorities were generally content to take the established Jewish communities at their word - when they bothered differentiating between Jews and Christians at all.
Later Roman and Graeco-Roman writers, as Christianity became more known and defined, would criticize Christianity both for its subversive nature (refusing to participate in common religious rituals of the Roman state and local communities) and its blatant disavowal of (what the Romans and Greeks saw as) an ancient and respectable religion (Judaism). Jesus himself would be condemned either as an unexceptional miracleworker of the type that occasionally gained fame in the near-east, as a charlatan or sectarian troublemaker, or as a Jewish religious teacher whose teachings were corrupted by later followers.
As such, when Jewish communities by-and-large condemned new Christian cults as a bunch of troublemakers spreading nonsense, Roman authorities were generally content to take the established Jewish communities at their word - when they bothered differentiating between Jews and Christians at all.
People need to remember that Jesus was a jewish mystic, and had more in common with the likes of Smith Wigglesworth or Jack Coe than anyone else. It should also be noted that at that particular time, there were a alot of other jewish mystics/prophets/apocalyptic preachers/messianic claimants/faith healers/miscreants.
the mainstream jewish leaders treated Jesus as a heretic… because he was.just like all the others we’ve forgotten about. (though we remember some of them. like John the Baptist…)
The romans only cared about Jesus when he said he was “king of the jews” and that was seen as rebellion against the roman empire- and it should be noted that by “the romans” we really mean the roman government overseeing that particularly small corner of the roman empire.
As for later christians and Rome… Nero blamed them for the bullshit that was happening in… exactly the same way Hitler blamed the Jews, or Trump blames refugees/migrants/immigrants. this wasn’t a religious thing. this was just a convenient scapegoat for rome being sacked and burning.