The exact same thing happens with any pose that isn't looking straightforward. I wasn't having this problem yesterday. It worked perfectly. I have no idea what I changed.
I've tried unticking/ticking No Location translation. All modifiers are applied or removed. Helper geometry and jointcubes are deleted. I'm using the default skeleton.
It looks like portions of the head and face aren't correctly weighted but I looked at that and they seem correct. I'm stumped.
Edit:
Okay. I think I'm using it wrong. I thought you could possibly change poses in Makehuman and then transfer them to a Pose Library in Blender. If the pose is already set in Makehuman, the model looks fine when imported. It only falls apart if the pose is changed and the skeleton is synced again.