As you said, it is a WPML bug. They don’t have a work around for me. They reported it as a bug and hopefully next versions of buddypress multilingual plugin won’t do the same!
You did a good job helping me confirm that the problem is not with buddypress but it comes from WPML.
Thank you.
You can consider this topic closed and the client is satisfied. (…unless you want to help me find a work around!)
