Your logic escapes me. We are talking about a corporate institution, not the body of Christ. Paul was a Jew but was he a Pharisee or a member of the Sanhedrin as a follower of Christ? Clearly not. Judaism, like Christianity, is a religious movement, not an institution.
Take your question deeper, and you’ll see where I’m coming from.
What “corporate institution” of Judaism was Paul a part of? Christ?
That’s my point.