I can speak to the Roman aspect of this! I believe the view of raw vs. cooked in the Roman period was more a cultural issue than a dietetic one- but nevertheless we see a strong preference among the Roman elite (for whom we have the best evidence) for cooked, mostly boiled and stewed foods. I think our best examples of this can be found across the text De Re Coquinaria, sometimes attributed to Apicius (who, I'm fairly confident, was not the author), which will always discuss meats in a cooked, typically boiled, manner (using a variety of verbs to discuss this process, such as ferveo, bullio, elixo, and decoquo, which all roughly represent the idea of boiling).

We can also see the Roman interest in their preparation methods in how they judged non-Roman cooking, typically using a hyperbole and depicting them as eating raw meats. A few examples of this:

Ammianus Marcellinus (when speaking of the Huns):
"But although they have the form of men, however ugly, they are so hardy in their mode of life that they have no need of fire nor of savory food, but eat the roots of wild plants and the half-raw flesh of any kind of animal whatever, which they put between their thighs and the backs of their horses, and thus warm it a little."

Corippus (when speaking of North African 'Moors'):
"Then the ram, the one hope of the fleecy herd, would fall prostrate at his feet as he panted. With unsheathed blade he would tear away the tight skin with all its great weight until the flesh lay open and exposed. The entire animal would be cut up into small 12 pieces so that he could twine the trembling limbs on spits and bum the ugly carcass over a scorching flame. Even as the fire burned he would attack the half-cooked meat, panting and fearless, and consume it all with savage jaws."

I don't suppose that these are necessarily examples of non-Romans eating raw meat, per se, but rather an example of the Romans being hyperbolic in describing a form of cooking which isn't 'endothermic'. For endothermic (literally cooked on the inside), you can picture a slow roasted meat which has been cooked very thoroughly and evenly; this is in contrast to exothermic (lit. cooked on the outside), where an example would be a medium-rare steak, where the outside is nicely seared, but the interior is in a rawer state. The Romans were endothermic cookers! But, this may show us that many other people were exothermic cookers in this period, and perhaps did see some level of rawness in their diet. Probably the clearest example of this comes from an early sixth century author, Anthimus (an Eastern Roman), who wrote a dietary letter to a king of the Franks, named Theuderic. In the introduction, Anthimus says the following:

"I would say that if a fire can be lit and if there is time, what has been suggested ought to be possible. However, if force of circumstance compels one to eat meat or anything else raw, then eat sparingly rather than excess."

He write further down, "Perhaps there will be asked the question of how it is that other peoples eat raw and bloody meat and yet are healthy. The answer is that these peoples may not really be healthy, because they make themselves remedies; for when they feel ill, they burn themselves on the stomach and the belly and in other places, in the same way that untamed horses are burned. My explanation for all this is as follows: these people just like wolves eat one sort of food rather than a variety of foods, since they possess nothing but meat and milk, and whatever they have they eat, and they appear to be healthy because of the restricted nature of their diet."

Saying this to the Frankish king, Anthimus is clearly trying to make a point against eating raw meats, which he interprets as being of the custom of the Franks. However, we see through the recipes which follow in the same letter than in fact this probably isn't raw in our sense of the word, but simply cooked in an exothermic sense. Here's a helpful quote for understanding how Anthimus approaches his recipes:

"The fresher the boar, the lighter it is, but it should be eaten boiled. It is is roasted, it should be placed some way away from the fire and for a long time, as we explained in the case of mutton" (Anthimus' 8th recipe).

We see the importance in the details when roasting for Anthimus, as he argues that if the boar is to be roasted, it should 'be placed some way away from the fire and for a long time' (a line which is repeated a few times throughout his letter). What this suggests to me, at least, is that Anthimus was trying to combat the roasting which the franks may have been used to, which may have been a quick roast right up against the fire (similar to how we may barbecue today), resulting in an exothermic cook of the food.

So to sum up, people were certainly aware of the negative effects of raw foods, and Anthimus does a good job at demonstrating this as he tries to educate King Theuderic of the Franks. However, it seems that aside from the rambling about diet by Physicians, the Romans were otherwise concerned with how their food was prepared, to the point that the method of preparation was seen as a cultural indicator. That being said, I don't believe the 'barbarians' were running around eating raw chunks of flesh, as some Romans said they were. But instead were probably in the habit of a more 'exothermic' style of cooking. For instance, if you don't grow up eating raw steaks, a raw steak may seem particularly raw and distasteful to you; this is probably the case with the Romans and how they viewed non-Roman cooking, which itself was still 'cooked', just not to the degree that the Romans may have practiced. I hope this helps to illustrate a bit of the cooked vs raw, at least in the Roman period!