“But this I confess to you, that according to the Way, which they call a sect, I worship the God of our fathers, believing everything laid down by the Law and written in the Prophets,” – Acts 24:14
It is frequent in Paul’s Epistles that there are troublemakers, spies, or Judaizers coming into the churches and confusing the gospel. Typically there are references made to these persons as attempting to establish Jewish customs (especially circumcision) upon these new churches.
As the main verse above points out, to the Jews this new group, called “The Way,” was to them just another sect or branch of Judaism (Acts 9:2; 18:26; 19:9, 23; 22:4; 24:22). There were various branches of Jews all with differing degrees of adherence to the Torah and what we have as the OT. There were the Essenes, the Qumran, Nazarenes, Pharisees and Sadducees just to name a few.
The Jews hear about the spread Judaism by way of this branch “the Way” and go to check it out. Along the way they attempt to “help” add or fill in the gaps of what their founder “forgot to include” about Judaism (along with other motives). It would be like our modern Christian denominations (or rival Christian sects). A Christian church evolves in a community via some evangelist. Local Baptists (Methodists, Catholics, and what have you) go to check out the new church, and finding them somewhat babes and new to the Bible, step in to instruct them further in their own understanding.
The struggle within the early church was that the Jews are zealously excited for the spread of their religion by way of this sect. But they fight to keep that sect within the more traditional boundaries of formal Judaism. They don’t want Paul in their synagogues converting steadfast Jews to this sect, but they have no problem entering into Paul’s churches to convert them towards a fuller Judaism. Christianity has not formally broken with its Jewish roots yet, It takes Paul’s letters, clearly defining that the formalities of the Law have been abrogated and are no addition to, and so must be kept separate from the Gospel (see Galatians and Jesus teaching on old and new wine skins and the like).
Such distinguished lines are almost fully blurred again in our age, such that some Christian churches are more like synagogues, attempting to be more and more Jewish. Sects are just names, being without creeds and doctrines most churches are swayed by the pulpit into heresies that just have new names, or the people just don’t know the differences.