I did not see a solution to this problem anywhere I looked. But, the following solution worked for me. I wanted to share with others who run into this problem.
Problem -
You set your Bunge.net emblem to be your avatar. You realize it's ugly and want to set it back to an avatar as an avatar...instead of your emblem as an avatar. lol You select an avatar instead, scroll down to the bottom of the page and click the yellow "Save" button. It says "your changes have successfully saved," yet when you look at your profiles avatar it is STILL set as your emblem.
Solution -
1. Go to your profile page
2. Along the top bar click on Settings
3. On the settings page go to all of the avatars
4. Select a DIFFERENT avatar at random. Doesn't matter what it is. But it needs to be a different one then the one you actually want.
5. Click the yellow Save button at the bottom of the screen.
6. NOW, go back to the avatars and select the one you actually want and click the Save button again.
The above process (for whatever reason) jogs the avatar back to what you actually want. Your good!
NOTE:
To be thorough this was all done from a PC, not a mobile device. Also, before I did the above I was first on the PC when this happened to me. I than opened the Bungie app on my smartphone and tried changing the avatar there and this made no difference at all. So I than did the above after this and it worked. Happy gaming all!