First, a note on how the filter functions work. If a developer has something that they want to filter/let others filter, then they apply any filters they/others have to it by calling apply_filters(). If you have a certain function that you want to filter something with, you add your function to that filter hook with add_filter(). Of course it only does any good to add a filter to a hook if the filters hooked to that hook are going to be applied somewhere. In this case, you want to look for somewhere that BuddyPress is applying filters to the post content, and add a function to that filter hook so that you can filter it the way you want.
Because you will be displaying the full post, you need to filter the content when it is being displayed. BuddyPress applies the 'bp_get_activity_content_body' filter to the activity content before displaying it. So you want to add a function to that filter that will return the entire post body:
function my_bp_full_posts_in_activity_feed( $content, $activity ) {
if ( 'new_blog_post' == $activity->type ) {
$post = get_post( $activity->secondary_item_id );
if ( 'post' == $post->post_type )
$content = apply_filters( 'the_content', $post->post_content );
}
return $content;
}
add_filter( 'bp_get_activity_content_body', 'my_bp_full_posts_in_activity_feed', 10, 2 );