A lot can be learned from Steve Mason's article on the origination of the term Judaism. I was unaware for instance that the term Judaism stems from a Greek word Ioudaismos which is almost exclusively Christian in its usage. Prior to the 337 appearance in Greek Christian texts, the only instances in Jewish literature are 4 in 2 Maccabees and 1 other in 4 Maccabees. (2nd and 1st century BCE respectively).
The author argues that the instances in 2 Maccabees demonstrate not a 'religious' use of the term but rather a practical cultural one. He compares the term Judaism to the term baptism - the latter meaning to baptise, the former meaning to Judaise. I.e., Judaism is used initially to mean the promotion and inculcation of Judaean culture and practice, in opposition to Hellenism (Hellenismos; also a term 2 Maccabees uses).
Of course, we are wise to remember that 'religion' is a relatively modern invention. Previously a peoples' 'religion' was inseparable from their culture. It was not a facet of life, but completely integrated into day to day and year by year living. The author argues that not only is 'paganism' as a religion or ideology a Christian invention, but so is Judaism as a religion. For writers such as Philo and Josephus, what they were describing was not an ideology but a living civilisation which contained and embraced philosophy, politics, commerce, festival, ritual, marriage etc.
Another interesting sideline that the author throws in is that Christianity faced much trouble during its first two centuries, precisely because there was no convenient social category as 'religion' - the Christians were a way of life without a history or homeland, more akin to a private club than the other cultures we may now characterise as 'religions'. Modern terminology makes invisible the vast categorical differences between these systems. Christianity thus appears to have been one of the first fully 'transferrable' ideologies (it occurs to me that Buddhism shares in all the same esential qualities also - predating Christianity by 600 years or so). Whereas nowadays we can easily comprehend what a 'religion' means in our society, and understand how it operates as a factor within multicultural society, a new ideological movement springing up from nowhere two thousand years ago would have been met with bewilderment by the populace. The same is clearly true in the early history of Islam, when Muhammad renounced the tribal practices of his forefathers in order to promote his monotheistic vision. 'Religion', it was claimed in both cases, was not something portable, not something that could be detached and passed around between individuals but a tradition and way of life that we inherit from our culture.
Of course, one is wise to know the difference between 'Christianity' (the ideology of the early church) and the teachings of the prophet Jesus. Jesus never intended to begin a new 'religion' (as we have seen, there simply was no such category in those times). His attempt, as best we can reconstruct it, was to refresh and revise the practice of Judaean culture in the face of the challenges from the Roman empire and Hellenic culture. The ideology of Christianity is largely a creation of the apostle Paul and the church which he made from the Jewish-Christian sect.