So yeah, that is what I have expected. It is a local install problem (maybe something went wrong during upgrade). Please talk to RL support. You may refer them to this thread for clarifications. Good Luck!

Okay, I just imported your model to Blender and it worked fine.... Aaargh!

Gee, I just saw the size of the texture folder. A whooping 255Mb per character!
6 files of 64bit PNG for micro-normal in each. Why in the world it has to be 64 bit!

This is odd, to say the least, and it makes me wonder if the same thing could be happening with some of my issues.

That is very possible. That is why it is best to confirm with those I have sent and then open a ticket.

There, try to import them to Blender. Those are Caleb exports I just did out of CC
https://www.dropbox.com/s/5e6fr15p49wqt8z/Caleb_Exports_CC33.zip?dl=0

Hmm... that is strange. I'd suggest opening a ticket with support as it seems to be a problem with your local CC installation.
Because I do not have a problem with either Bind-Pose or Current Pose Export/Import of Caleb

Yes, I saw that thread, I think I got them conflated. Reading through it though, it's interesting that people with the same versions are having different experiences. This is odd, to say the least, and it makes me wonder if the same thing could be happening with some of my issues.

This is a CC3 figure I exported as OBJ a couple of months ago. Exactly the same procedure in both CC3 and Blender as the previous shot.

That is a little different. It is about exporting characters converted to Game Base. There is also another thread started by the same user, where I have shown couple of workarounds for exporting/importing Game Base characters.
That is by exporting from iClone and if you do not have iClone changing bones orientation settings on import in Blender. https://forum.reallusion.com/448830/Is-it-possible-to-export-CC3-character-with-bones-connected-so-I-can-animate
Bone orientation on Game Base export was confirmed by RL and fix should be released at some point.

This is the stock Caleb figure with no changes, exported as an OBJ and imported to Blender.

There's also a thread from a couple of months ago about FBX problems with Blender, which RL has acknowledged is a CC problem, but as far as I can tell, hasn't fixed.

https://forum.reallusion.com/448552/Please-help-me-exportimport-CC3-to-Blender