Though this doesn't necessarily mean that skipping is what *truly* causes this. For starters: Last night when things glitched, I did a full party level up and this time I brought everyone over to Withers and then leveled them one at a time.
I doubt it's the case. Since I never skip anything during level ups and still get it.
Also, I've seen it occur when buffing someone with Longstrider. Literally, their portrait was fine, I cast Longstrider on them and the portrait was borked.
Such an occurance leads me to consider it might have something to do with applying effects to a character causing the portrait to have a chance to be changed to an invalid parameter and thus going to a "Default" setting. Of which "Leveling up" provides the most effects to a character and is thus more likely to cause an interaction.
Either way, the root cause would likely reside somewhere in the portrait parameter being affected by something other than the intended mechanisms (I.e. The character creation options you use when making a Tav/Durge/Hireling things like Wyll getting his horns or Shadowheart dying her hair)