When we talk about those feasts, though, we are normally talking about Easter, Epiphany, Christmas, Baptisms (and all appropriate days for them), and All Saints' Day (the day we celebrate the whole body of Christ Jesus). All those days are rooted in early Christian traditions. They also recognize different parts of Jesus' life, and through Baptism, our partaking in them.
Christ the King is much more recent. It was started by the Pope Pius XI, the Bishop of Rome, in 1925. Originally it would have been held in late October, very close to celebration of Reformation Day. Thus it is likely that this was a Roman Catholic response to a Protestant celebration.
Christ the King was not originally celebrated in The Episcopal Church at all. In fact our 1979 Book of Common Prayer does not list it. As far as the Prayer Book is concerned, today is not Christ the King, but The Last Sunday after Pentecost.
As time passed, several denominations came together to use the same readings and thus creating The Revised Common Lectionary. This included Roman Catholic and Protestant denominations working together, and slowly Christ the King made its way more firmly into Episcopal practice.
There is nothing wrong with the idea of Christ as King over the world, because it is true. The readings we have in our lectionary now relate to this idea of Christ's kingship, and it fits well with the themes of Advent, which starts next week. But does this day deserve white as its color?
It depends on who you talk to. Because it is a more recent celebration in the church, I would say no. Plus we want to emphasize that this is the end of the Season after Pentecost more than anything.
I would also say no and object to throwing in the title of Christ the King for this Sunday because we as Episcopalians are not Roman Catholic, nor are we fully Protestant. We live in that middle area often referred to as via media. If we were to celebrate Christ the King in its full Roman Catholic glory then we should also celebrate Reformation Sunday. I say it's better if show that our allegiance is truly with Jesus Christ and no other by not celebrating either day. So for the time being, I'll be following the Prayer Book and saying this is The Last Sunday after Pentecost, nothing more, nothing less.
Further Reading:
Alexander, Neil. Celebrating Liturgical Time. New York: Church Publishing, 2014, pgs. 42-43.