BuddyPress.org

Yes, this can be done in code. You’ll need two filters. One removes the unwanted items from the dropdown on the activity page, and the other removes them from the activity stream itself.

add_filter( 'bp_get_activity_show_filters_options', function( $filters ) {
	unset( $filters['friendship_accepted,friendship_created'] );
	unset( $filters['new_blog_post'] );
	unset( $filters['new_blog_comment'] );
	return $filters;
} );

add_filter( 'bp_before_has_activities_parse_args', function( $args ) {
	$filter_query = array(
		array(
			'column' => 'type',
			'value' => array( 'friendship_accepted', 'friendship_created', 'new_blog_post', 'new_blog_comment' ),
			'compare' => 'NOT IN',
		),
	);

	$args['filter_query'] = $filter_query;
	return $args;
} );