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Low intake of saturated fat and high intakes of vegetables, fruits, whole grains, legumes, soy products, nuts, and seeds (all rich in fiber and phytochemicals) are characteristics of vegetarian and vegan diets that produce lower total and low-density lipoprotein cholesterol levels and better serum glucose control.

Compared to what though? If you only eat properly selected (fat to protein ratio) meat products (fatty meat, eggs, hard naturally maturing cheese) with a proper selection of vegetables, so that they contain all the micronutrients you need in good quantities, fiber and are low on carbs, the amounts of carbohydrates you 'll be getting will definitely be low enough to have perfect serum glucose -most of your energy will be coming from ketone bodies. You can't have elevated serum glucose if you don't rely on carbs for energy. It's pretty tough to mess up the metabolic pathways related to carbohydrates too with that approach. Which is pretty easy to do if your focus is to just eliminate animal products, since most plant foods are loaded with carbohydrates. When the objective is health, the focus should be proper selection of foods for the body first and then everything else.

Of course vegetables (fiber), fruits (water & fiber), whole grains (fiber), legumes (fiber), soy products (debatable, tofu, tofu skins, tempeh all have low to zero amount of carbs), nuts/seeds (fiber) are handled better as far as their carbohydrate content goes since they are metabolized at a slower pace than white rice or flour products. But it's not the meat in the burger that messes up your glucose levels, its the potatoes and the bread. And if you don't match your activity levels with the quantities of -easier-for-your-body- carbohydrate sources from plant foods, you will start having issues too, quantity matters as much as quality in this aspect of nutrition.

This is not a comment to support animal products, just to point out that what messes up serum glucose is improper selection of plant based foods, not saturated fat or meat products in general (probably with the exception of many dairy products).

You can also just as easily find widespread deficiencies in important things mainly or only found in plant-based foods like fiber

There are other deficiencies too if you don't eat proper plant based foods (again like the ones mentioned in the first quote of my comment), which can be equally important. Easiest example is magnesium. All the greatest sources of it are plant based foods. This metal is also a good reason why legumes/beans are important (apart from the obvious abundance of potassium). Seeds and nuts are a great source too, but cost more (not just to buy them, they take up much more resources from the environment to produce them).

People who rely heavily on meat, thinking this is easy access to full of essential amino-acids protein (which it is, muscle tissue is something of a protein storage for most of animal bodies), won't be getting magnesium in good quantities unless they start eating proper plants or buying supplements (created from plant matter), since most of magnesium (and many other micronutrients like it) is stored in the bones of the animals (which we don't eat, and bone broths don't do much either). It's pretty funny that many people think they can't get proper protein from plants, which is untrue, but in fact it's the other way around, as far as deficiencies go, once you start looking at micronutrients.