I went on a carnivore diet (no carbs, no plants) and my clusters are much weaker, a trigger (2nd hand cigarette smoke) is nearly suppressed too.

If I reduce fat intake significantly too, so that I only consume proteins I with very little energy intake for days/weeks (rabbit starvation) I actually completely suppress the CH attacks. I only notice the activation in my head but nothing happens - no pain, no other issues - it is laughably funny. So no, in my case protein is not a problem, energy is.

Sadly it is very difficult and not healthy to avoid energy, so I stopped doing it. Only when the attack is nearing I try to avoid energy again, but it is not as good as being abstinent for days before the attack. Also water fasting is not nearly as good as only consuming protein for suppressing the attacks, which is strange.

Besides: My chronic painful lipoma does not hurt anymore because I don't eat plants anymore and digestion is partially better too, but gastritis is worse because of issues with fat digestion.