Is the false teaching in Galatians still relevant today?
Yes. The false teaching Paul refuted in Galatians was not confined to his day; it has plagued Christianity through the centuries and remains just as applicable today. Believers still contend with the subtle false teaching of legalism, which appears in many shapes and forms rather than only temple worship or Judaism.
In Galatians, Paul is shown refuting false doctrine rather than merely defending his apostleship. The context stresses that doctrine is primary; without doctrine, you have nothing. Though experience is emphasized today, experience does not set your feet in concrete—doctrine does. The false teaching that crept into the Galatian churches, and every church Paul founded, was not unique to Paul's day. It has plagued Christianity up through the centuries and is just as apropos today as when he wrote it, because legalism is still constantly fought. Legalism is normally thought of as temple worship and Judaism, but it comes in all kinds of subtle shapes and forms.