Adding the code below to my bp-custom.php file removed the last active status on one of my sites

add_filter( 'bp_nouveau_get_member_meta', 'ps_remove_last_active',10,3 );
function ps_remove_last_active ( $meta, $member, $is_loop ){
	$meta['last_activity'] = '';
	return $meta;
}

https://buddypress.org/support/topic/remove-last-active-status/