This response by u/AisleOfTextusPeach answers your question neatly.
Basically Judaism was recognised as an ancient respectable religion tied to a particular ethnic group with whom agreements had already been made.
Christianity was regarded as a new radical offshoot of Judaism that was not tied to an ethnicity. Therefore the refusal of non Jewish Christians to worship Roman gods was not them invoking a traditional religious obligation, it was a collection of ordinary Roman citizens defying the emperors authority. This was especially important as at the time civic religious rituals were an important part of public life.