I may be splitting hairs with my take on it (but then we are looking at one word, so maybe not). I think it has to retain the "the." King Charles can (and should) defend the right to and respect of multiple faiths, but saying you are the "Defender of Faith" is basically saying nothing at all.

For example, as a Catholic, I can defend the rights of people to hold other beliefs, but I cannot really defend beliefs that I do not hold. If you simply called me a defender of faith (no faith specified), it implies that I can defend all faiths equally, which I logically cannot if I am not an adherent. The original title came (ironically) as a result of Henry VIII's defense of Catholicism against Luther, so it has a specific point of reference.

If you remove the "the," it means the King defends Catholicism as strongly as he does Anglicanism, which if true would be the end of Anglicanism. Perhaps rather than removing the one word, other words should be added, like "the right to."

All that said, I also like it the old way because it just sounds cooler and more traditional.