Why were early christians harmful to román empire

The claim was highly exaggerated by medieval christian apologists to deflect from so much of their early history of competing sects of Christianity killing each other off. Learning about the Gnostics for one example. Actually, the Roman and Jewish record and archaeological evidence clearly occupation government against the jews. 

So basically because the Romans felt that only their culture should be and religion should be spread. And that anything outside their culture was bad.   

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