The best suggestion I could find is here:
Exclude specific users/usergroups or forum sections from activity stream?
Pay particular attention to posts #4 and #15 by Lynne.
Because there appear to be no relevant plugin hooks and query strings, this will unfortunately require core file hacks.
You could wrap the relevant activity stream templates in conditionals, but I suspect that may throw off the displayed number of elements grabbed via the "More Activity" link. I think the best solution is to alter the query as Lynne suggests rather than hide posts after they have been retrieved from the db.