For personal evidence, my CRP is very low and I regularly get 70% or more of my calories from fat. Daily. I'm sure it has occasionally, on a very high-protein day, dropped to something like 50%. But if fat were going to be inflammatory to me, it would have by now - and my CRP would be high. But it's not. Doing this three years.
Steak, eggs, potatoes - fruits, nuts, berries and forage. Coconut milk and potent herbs and spices. Tea instead of coffee now and teeny amounts of kelp daily. Let's see how this does! Not really had dairy much, and gut seems better for it.