It seems to me that CC offers some odd export choices...

iProject - no issue there. Makes sense. 
iAvatar - no issue there. Makes sense.
FBX - Locked down to 3DXChange Pipeline users only. Makes sense. This is as per the 3DXChange rules.

However, why does the Export OBJ only offer Nude Character? According to the 3DXChange rules, users with 3DXChange Pro are able to export to OBJ. This is supported by the fact that you can save the character, with clothing, as an iAvatar, then open it in 3DXChange and then export to OBJ (or parts of it to OBJ) if you have 3DXChange Pro (or Pipeline). So why not make the Export OBJ option available directly from CC similar to Export FBX option?

Since RL makes the FBX version of the Nude CC character available to developers on their website (for developers with 3DXChange Pro who need the CC armature to create clothing), it seems to me that instead of
Export OBJ | Nude Character, the option might have been intended to be Export FBX | Nude Character (as an alternative way to get the nude FBX file).

From the fact that you can still export the character with clothing as OBJ through the 3DXChange application, I don't think it was intended as a feature limitation imposed on 3DXChange Pro users.



"We often compare ourselves to the U.S. and often they come out the best, but they only have the right to bear arms while we have the right to bare breasts"
Bowser and Blue, Busting The Breast

I do believe the OBJ export is intended for sculpting software like Zbrush, Mudbox, etc hence the quad export. FBX is more for the clothing workflow. At least that was my assumption. 

Free Range
My IMDB

Probably correct. But why just "Nude Character"? Why not have options for Character or Selected Item?



"We often compare ourselves to the U.S. and often they come out the best, but they only have the right to bear arms while we have the right to bare breasts"
Bowser and Blue, Busting The Breast

Good question for which I have no answer, haha. I would definitely hit up support and see what they reply with.

Free Range
My IMDB

The answer is quite clear. It's the same reason you can't export CC body morphs (easily).
How familiar are you with "Parsing?"