I had this same error, “There was a problem cropping your avatar”. After trying many things, what finally worked was installing php5-gd and do a restart.
On Debian:
apt-get install php5-gd
After this, usually people restart Apache server. But in this case there was Nginx server instead, and restarting it wasn’t enough. A PHP restart was needed.
So, I went to Webmin control panel to restart the Nginx PHP fcgi server:
System > Bootup and Shutdown > php-fcgi-…
And avatar cropping started to work for BuddyPress groups, profiles…
