Why did Rome try to stamp out early Christianity?
Rome respected ancient religions, including Judaism, and tolerated it as an ancient faith. Christianity, however, appeared as something new under the Roman Empire. Because it was not an ancient religion, Rome tried every way to stamp it out, which brought Christians massive persecution while Jews largely avoided it.
Les explains that Rome had a lot of respect for ancient religions, including its own mythologies, and Judaism was an ancient religion. Rome therefore put up with Judaism, even guaranteeing safe delivery for Jewish offerings sent back to the temple in Jerusalem and giving Jews permission to put their own people to death. Christianity, by contrast, was not an ancient religion when it appeared under the Roman Empire. It was something new, so Rome tried every which way to stamp it out, and that is why Christians came under such massive persecution under Rome, while the Jews did not.