Sorry, but I'm going to nitpick. I think the word "allowed" creates or reflects the wrong mindset. I can think of at least two alternative approaches that people take in defining paleo diet.
1) You have a health goal. So you consider the (especially evolutionary) arguments that support or undermine the value of a choice like eating dairy or eating fermented dairy, and make your own decision. Many who construe paleo in this way consider at least some dairy to be paleo-compatible, because its constituents are mainly the same as other paleo foods. Since fermented dairy is tolerated by more people, and has the added benefit of probiotics, it is even more likely to be considered to have a place in a healthy diet than dairy in general.
2) You want to understand what paleo people probably ate, and replicate that. Getting non-negligible amounts of milk from an animal almost certainly requires domestication. If paleo is defined as pre-domestication, then no dairy can be paleo. If you argue that some form of domestication that allowed milking could have occurred in paleo HG's, or if you define paleo as extending later into history, or some other argument, you add dairy to the list.
As best as I can tell, the dairy issue isn't so much a debate but rather an individual issue.
Some will tolerate casein and lactose without issue. They don't get bingey eating diary, or suffer inflammation, or get 'addicted' to it. For them, it's a convenient source of protein and saturated fat.
Others simply don't tolerate casein or lactose very well. They may suffer systemic inflammation or have poor gut tolerance of dairy products. It may trigger bingey/hungry behavior, weight gain, or stall weight loss. They shouldn't eat it.
Many who don't tolerate most dairy do ok with heavy cream due to it's exceptionally low casein and lactose content. Most do fine with butter.
It can be confusing because dairy remains something of an unresolved debate amongst Paleos; some see it as a Neolithic agent of disease, others as neither optimal nor harmful and some believe it to be beneficial.
Those that do eat dairy (lacto-Paleo) tend to prefer full fat, raw, grass-fed and/or fermented dairy like Greek yoghurt, believing that this minimises any negatives whilst heightening the positives.
Two weeks ago, I ate greek yogurt one day, had cramps,and tried again the next day and kaboom! I was in pain and felt that a lump was trying to pass through my system. It took several days of a lot of liquid but no food to clear. So, even though before paleo one month before I was having yogurt (plain) and cheese sometimes with no problem, I decided that it was not for me anymore.
Kale and other calcium rich foods will be my mainstay instead.
I can eat dairy all day with no GI problems, but without a doubt it puts weight on. I'm using it right now for that very reason as I am currently trying to gain weight during a bulking cycle.
Dairy has been shown to create a much larger insulin response than would be expected by its lactose (sugar) content. This makes sense given that insulin is a growth stimulating hormone and milk is designed for baby animals.
I don't see anything wrong with dairy provided you don't have an allergy or intolerance to it. To me, paleo is not about eating exactly WHAT Grok ate, but eating HOW he ate, which would be in such a way that you get full nutrition, keep your insulin levels down and avoid all the added non-food garbage that's in processed foods. Grok's diet had those qualities and I feel that is what we are shooting for, not an exact replica of what he ate. Otherwise why aren't we all eating bugs and worms too? I'm pretty sure those would have been a part of his diet.
I think one reason dairy is confusing is because it should really be broken down into several categories:
Milk - tons of lactose and gives some people problems; high glycemic index.
Butter - how often do you hear a paleo say they don't eat dairy, then say they cook with butter; it's still dairy isn't it?
Cheese - contains almost no lactose; low glycemic index.
Cream - identical to milk in most ways except thicker, low lactose and low glycemic index.
And then of course, there is dairy from different sources--cow, goat, and so on--which all have their own unique attributes.
Dairy is such a broad term that it makes more sense (imho) to think of it in sub-categories instead of super broad terms.
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