I managed to circumvent the bug by creating a new career, then immediately switched back to my old career, and was able to change emblems again. For some reason the Side Emblems appear under UBOAT options again when I do this.
After changing the emblem, I deleted the new profile.
I think I have to create a new throwaway career every time I want to change the emblem on my old career, so it's not a very elegant fix.
If anyone knows a better way or has experienced this bug with GWX, let me now.