This is a smaller group of people within a larger group. Christianity was originally considered to be a small group within Judaism. See how you translated "sect" in [Acts 24:5](../24/05.md).
Paul uses the phrase "in that same way" to mean that he, as a believer in Jesus, serves God the same way as their Jewish ancestors did. He is not leading a "sect" or teaching something new that is opposed to their ancient religion.