Its the word "feud" I find so annoying. Feud is a pretty big word. And frankly is pretty unlikely. Tension? Sure. Struggling to adjust to the new dynamic? Absolutely.
But these are two women in their 30s who are married to men they genuinely seem to love, living their lives on the world stage. I simply can't believe they are are so petty as to be actively trying to destroy each other (which is what "feud" suggests). It took me years to settle into a happy relationship with my SIL, and I'm still working on it with my newest one, who has been with my brother for 5 years.
Personally, I think they should address it directly. But not in a palace statement. A joint event, and a joint speech, making some very pointed comments about bullying, family relationships etc. No need to be subtle. Polite, dignified, regal... absolutely. But they're strong confident women who I think have the right to actually speak out for themselves.