That’s strange, I use invite anyone on a number of sites so I can confirm it works.
Have you tried deactivating all plugins except Buddypress and Invite Anyone to see if that works?
If it does, it’s a case of activating the other plugins one by one until you discover which one is causing the conflict.
IF you are getting the 500 error you may not be able to get to the Dashboard to deactivate plugins, that being the case you should FTP to the wp-content/plugins directory and you can delete the other plugins from there in order to get your site back.
