Christ the King is one of those many feasts that was arbitrarily shifted with the institution of the Novus Ordo Mass. I find this regrettable. But we should remember that this particular feast was only fifty years old when its date was moved. I'm not saying that newer feasts are any less important than older ones, but I am pointing out that Christ the King was a relatively new feast, called up out of thin air and stuck in the calendar by Pius XI. Is that alright? Of course it is: the Supreme Pontiffs can and often have added new feasts to the calendar throughout the centuries. Christ the King was an admirable and worthy addition to the calendar and the focus of the feast was very pertinent and in keeping with Catholict theological tradition, as the document Quas Primas goes to great lengths to point out. I think it was a good and wholesome thing that Pius XI did in giving us this feast. Of course, this sort of thing ought never be done flippantly, and I don't think Pius did it that way; it was the product of much reflection and prayer.
Now, let's be honest, would we be so willing to accept a new feast in the calendar if a post-Conciliar pope were to add it? I was not a Traditionalist back in 2001 when JPII proclaimed Divine Mercy Sunday; I would be interested in hearing from anybody who can remember how the Traditionalists took the addition of this feast day. I don't see anything wrong with Divine Mercy Sunday, except perhaps that it obscures the traditional Low Sunday, which nevertheless was not a large celebration on the traditional calendar. Likewise, recalling that Christ the King was at one time an innovation, I accept this innovation made by the Church because it was in keeping with the theological tradition of the Church's history, it was made by the legitimate authority and it was a worthy way to combat the anti-Catholic mentality of the times. It was organic and a faithful reflection of the Church's perennial teaching.
I wanted to use the feast day to exemplify a mode of thinking I go by but that I know not all Trads do: for me, I do not reject something out of hand because it is new, but only because it is bad. My whole resistance to the circus that has grown up around the Novus Ordo is not simply because the NO is new, but because it is not good. Now, the extent to which something is bad because it is new is the degree to which the new thing breaks with Catholic Tradition. The Church has always accepted new things, but only in a slow, necessary and organic development that was always in consonance with what came before. Furthermore, though the Church frequently added new things, it never dispensed with old things (check out 1896 Apostolicae Curae of Leo XIII for an example of how the Church accumulated but never did away with anything for fear that it might be unwittingly discarding something essential to the faith). If I were alive in 1925, I would joyfully accept the institution of Christ the King because it represents a truly organic and faithful addition to the Church's liturgical life.
Can we say the same thing about the arbitrary movement of feasts after 1969, as if the calendar were the private property of the liturgists who happened to be alive in the 60's? What about the invention of the Luminous Mysteries that had absolutely no precedent in tradition and actually served to obscure the earlier tradition of associating the Rosary with the psalter? What about the liturgical innovation of self-communication? None of these things are organic. I reject them not because they are new, but because to some degree they are all not good because they are not consonant with tradition (the Luminous Mysteries) or in other cases (self-communication) are positive obfuscations of Tradition.
So, new does not necessarily mean bad. The way the Church adopts new things is always from a reflection of the old, demonstrating how the new is simply a restatement of the old. If, however, someone proposes something new that is set up in contradistinction to the old and as in opposition to it (i.e., facing the people versus "back to the people") then the novelty must be condemned for the very fact that it is a bad novelty.
A woman recently asked me why I wanted the return of the Old Mass. I thought of lots of reasons: I thought about how it is more reverent, how the Mystery is better expressed, how the congregation could receive more grace ex opere operantis, I recalled all of the abuses of the Novus Ordo, etc. There are many reasons why the Old Mass should be preferred. But in the end, I gave her one single answer, and I think this answer ultimately is the best one to the question:
Because it is what the Church has always done.