I did some troubleshooting while Teams desktop clients were not able to get the profile pictures from all others:
When looking for this more deeply, I noticed that Teams client is trying to download the profile pictures from URL starting with:
teams.microsoft.com/api/mt/part/emea-02/beta/users/8:orgid:f8ca...
Nice to see that I was volunteer for this (even not sure did I really accepted that) 
