In a sense, the Inquisitions did go after non-Catholics, if Protestants and Cathars and other Christian heretics are understood as non-Catholics.
The Inquisitions did not go after, say, religious Jews* or Muslims, and were specifically forbidden to do so (and why should they? The Inquisition was tasked with keeping order within the Church: Muslims and Jews are by definition outside of it). So, with qualifications, you are correct: the Inquisitions did not go after non-Catholics.
Christi pax,
Lucretius
St. Augustine, pray for us!
*The Inquisition (especially in Spain) did go after ethnical Jews (as opposed to religious Jews: Jews who practice what we call today Orthodox Judaism, as opposed to those of any religion with Jewishness ancestory), however, especially those who “converted” to Christianity for the society benefits. In their defense, it was hard to be a Jew in Spain in the 16th century