a recognized religious party: a group inside a larger faith, marked out by the teaching and practice it has chosen to hold
In Acts this is the ordinary, unremarkable word for a named party inside Judaism. The Sadducees are one, the Pharisees are another, and a first-century Jewish reader would have heard no insult in it. These were groups within the same religion, reading the same scriptures, differing over the resurrection, the law, and how strictly it should be kept. Paul can even speak with some pride of having lived by the strictest of them.
The sting appears only when the label is aimed at a movement whose right to exist is in question. In Jerusalem and again in Rome, people pin the word on the followers of Jesus, and the lawyer prosecuting Paul uses it to make them sound like a breakaway group rather than the true heirs of Israel's hope. Paul takes the word without flinching and then quietly changes the terms: he worships the God of his ancestors, believes everything written in the law and the prophets, and calls the movement "the Way".
Behind the noun stands a verb meaning "to choose". A party of this kind is defined by what it has picked out and holds to, which is why one and the same word can name a respected school of thought in one sentence and a damaging split in the next. Everything hangs on whether the choice was a legitimate one.