I apologize before hand if this rambles a bit: I was raised with Ayurveda and what you have to understand (through study) is that for every proscription provided there is also an antidote, for instance, certain branches of ayurveda proscribe tomatoes or nightshades, but then say: blanche, peel, seed the tomato (the seeds are said to be hard on the kidneys) and "treat" with turmeric while cooking to negate unwelcome effects. Likewise, you can antidote meats with kapha spices: cinnamon, cayenne & paprika, which "lighten" the density of the foods.
I have a vata-kapha prakriti & I also go in and out of phases wanting red meat. I love it in the winter but I also mix it up: lamb, seafood, chicken, beef, elk, etc. But I don't need much more than 3-6 oz most days unless I'm really active.
And you also have to understand that "eating according to dosha" doesn't mean you eat just one way all year. You don't just eat kapha foods all year round, that's horribly unbalancing. You have to eat seasonally. Today we are entering Kapha season, and what's available in spring time, what grows first?
Bitter greens, sprouts, strawberries, etc. What's left in your pantry? Following an ayruvedic diet meant to mimic what mother nature does.
If you're wanting to eat paleo in the winter regions, as our ancestors may have: you're going to need a lot more fat, proteins, root vegetables, fruit that might keep: apples, or dried fruits and nuts. Not a lot of berries unless it was already pounded into pemmican. Not a lot of broccoli or asparagus available in the January wilds. Whereas summer is full out abundance of green things, rich sources of carbohydrates and fish, herbs, etc.
It is helpful to make the distinction now, that describing doshas is really the art of observing the balance of three natural FORCES in one’s body. Vata is responsible for catabolism, (breaking down) Pitta, for metabolism (enzymatic) & Kapha represents anabolism (building). This balance is what allows an individual to experience & express health & wellness. Kapha, being the anabolic force, is said to have a predominance of "sweet" already in the body - i.e. they naturally have a tendency to "build more tissue."
It's not that they don't need protein and good fats, but the ratio needs are going to be different that a high-metabolic vata. And even if you balance and preventatively treat for Kapha metabolism, that person will never have the same metabolism as one of the other doshas. No matter how thin/fit a kapha person becomes, they will never appear as petite in bone structure as the other doshas.
Each dosha needs all the good stuff that paleo type eating recommends in the right Ratio. Each of them also need particular things to keep them each in balance, for Kapha: more vegetables and spice than a Vata needs, etc.
Cadu makes some good points as well, but doesn't take into account that sour foods are fine when taken in season, again it's not a 360 day eating design.