No idea how components anywhere works to output components anywhere so I've no idea why it's causing that, but my guess is it's not outputting the headers from CB resulting in the JS being missing. Note with CB Activity 4.0.0 you'll be able to have as many activity streams as you like. See the below blog post regarding progress.

www.joomlapolis.com/blog/kyle/18724-streams-everywhere-follow-everyone

CB doesn't alter the Joomla buffer (we do not get or set the buffer). Our headers are just echoed by our component file instead of output using Joomla API. The reason for this is we need stricter load order and noConflict control for our jQuery plugins than Joomla API provides. We do not echo the headers if &format=raw or &format=json. If components anywhere is using either to load in a component view then CB won't be loading in any of its headers and should be using &tmpl=component instead of a format, but again I've no idea how components anywhere is outputting a component view.

I'm not sure what this has to do with CB Activity module though. If you're not loading in CB Activity module using component anywhere (you shouldn't need to as you can use loadmodule ) and it's still breaking CB Activity module then I've no idea what components anywhere is doing to the buffer.