Not exactly. They still considered themselves Jews. When Paul was arrested he identified as a Pharisee. (present tense, not past tense)
That was to defend himself concerning teaching a resurrection and he wanted the Pharisees to side with him against the Sadducees. He was not a Pharisee once he converted to Christianity. He also later in Acts referred to being a Pharisee in the past tense and recounted what he used to do against Christians.
It was what Paul taught against the practices of the Jews that made Jews want him dead including Pharisees. Paul gave up his old Pharisee ways for new Christian ways and he was beaten by the Jew many times for what he taught.
2Co 11:23 Are they ministers of Christ? (I speak as a fool) I am more; in labours more abundant, in stripes above measure, in prisons more frequent, in deaths oft.
2Co 11:24
Of the Jews five times received I forty stripes save one.
Gal 1:13 For ye have heard of my conversation in time past in
the Jews' religion, how that beyond measure I persecuted the church of God, and wasted it:
Here he speaks of the Jew's religion as their religion, not including himself as part of their religion. This is because he practiced a different religion than the Jews.
Gal 1:14 And profited in
the Jews' religion above many my equals in mine own nation, being more exceedingly zealous of the traditions of my fathers.
Gal 1:15 But when it pleased God, who separated me from my mother's womb,
and called me by his grace,
Gal 1:16
To reveal his Son in me, that I might preach him among the heathen; immediately I conferred not with flesh and blood:
Gal 1:17 Neither went I up to Jerusalem to them which were apostles before me; but I went into Arabia, and returned again unto Damascus.
And this speaks to his religious and spiritual conversion to Christianity.
