A 500 error is a server error, probably has nothing to do with BuddyPress.
If your server doesn’t have curl or a complete PHP 5 setup (it’s not totally uncommon, I’d say maybe 5% of installs), then it may not support the type of code in the Facebook PHP library.
What hosting service are you on?
I was getting similar 500 error on other php plugins (for example, Browser detect) when using Windows hosting and WordPress. While WordPress can operate fine on Windows hosting, the full potential of most of the plugins won’t be available.
Also, if you have any other Facebook-related plugins, deactivate them first. Multiple Facebook plugins will almost always conflict with each other.
Closing this out since there’s been no follow up. Please open a new thread if this is still an issue. Thanks