I'm also having this issue, I've taken a few steps to resolve it which have been unsuccessful. I've tried:
- restarting the device
- turning off full access, restarting the device, then granting full access again
- logging out of bitmoji, restarting the device, logging back in
- deleting bitmoji, removing the app, downloading it again, then logging back in.
The app itself works, and loads my images - however it will not work within messages.
My wife upgraded her phone at the same time, with the same phone model and hers appears to be working fine. The only two things I haven't done yet is reset all settings and erase all content and settings.