Diogenes puts it succinctly.
So the Knights of Columbus won’t go further than the bishops go. If the bishop hasn’t excommunicated Senator Mengele, the Knights won’t suspend his membership. If the bishops say it’s OK, it’s OK with the Knights.
So if the K of C had been active in England in the 1530s, following the same policies, would they have followed their bishops’ lead in accepting the title of King Henry VIII as legitimate head of the Church in England? Or would they have supported a lonely layman who rejected that claim?
Thomas More, you will recall, was a Knight– although not of Columbus. Today he’s generally known by another title, having gained membership in a still more elite fraternity