In Witcher 3 I see men in nothing but underwear looking like a big cloth diapper. Was this clothing common in medieval Europe?

by Turband
Beltharean

The article of clothing you refer to are known as braies or breeches and were, essentially, the predominant male undergarment throughout the medieval period. Later on a type of short braies were developed that are more akin to modern briefs, mostly because of changing fashions. Loose garments like the tunic gave way to more form fitting hosen, doublets, and arming coats.

More immediately addressing your point though, in most instances where you actually see braies, the person being depicted is doing some form of manual labor. They've generally removed a garment either because of heat, or to facilitate movement, one example being the image I linked above.

Here, the two workers on the right have loosened the rear ties on their hosen, revealing their braies; Unlike modern leggins wool only has so much stretch to it, even when cut on the bias, so during physical activity when you need to bend over often it's often necessary to loosen the back ties to give a full range of motion.

This is another example of people having removed all other garments while working.

As I touched on, generally these wouldn't have been seen in every day life, particularly for nobility or the wealthy. It's rare that you'll see a depiction of a nobleman with his braies showing unless the artist is trying to make some sort of critique about the individual. In any case, I'd say the only sort of anachronistic aspect to it is that most of the fashion in the witcher, which is rather form fitting with tight-waisted doublets, codpieces, plaque-belts, etc. is from the late medieval period, when the loose flowing braies had mostly fallen out of fashion. That's not to say they weren't ever worn, but they'd probably be considered a bit antiquated.