Hi everyone… I’m joining this discussion late, but I think I can offer some help… From my own personal experience it definitely was a conflict between /js files (jquery).
I installed buddypress and the cropping worked fine, then I did some custom work in the code (none related to buddypress) that needed jquery (thereby needing a link in my main header include to the /js folder for the source). When I went back to test the cropping feature, it did not work. I had the same problems that have already been stated here. My fix was relatively easy because my jquery was only needed for the home (index.php) page, so I removed the for my custom jquery from the header (NOT THE BUDDYPRESS) and instead added it to the body of my index page. Once I removed the jquery I added, the cropping worked again like a charm.
I assume (actually I’m pretty sure) buddypress uses jquery for croping the images and therefore other scripts that use jquery might conflict. This could mean any jquery widgets might interfere (even drop-down menus, sliding galleries, etc)… If they use jquery, you may have a problem —- at least that is what I found out for me.