The ICKSP in their own words:
“The Institute of Christ the King Sovereign Priest is a Society of Apostolic Life of Pontifical Right whose goal is the honor of God and the sanctification of priests in the service of the Church and souls. Its specific aim is missionary: to spread the reign of our Lord Jesus Christ in all spheres of human life. Our work is carried out under the patronage of the Immaculate Conception, to Whom the Institute is consecrated.”
Which basically means that whilst about the Lord’s work in His Vineyard, they also get to set their own rules about what colour hat they wear whilst they do it; naturally, we approve.
More soberly, information regarding the excellent work of this august society can be found here: