Many reconfigurable network topologies have been proposed in the past. Efficient routing on top of these flexible interconnects, however, still presents a challenge. In this work, we reevaluate how key principles that have guided the designs of many routing protocols on static networks perform on reconfigurable network topologies. Based on theoretical analysis of key properties that routing in a reconfigurable network should satisfy to maximize performance, we propose a topology-aware, globally-direct oblivious (TAGO) routing protocol for reconfigurable topologies. Our proposed routing protocol is simple in design and yet, when deployed in conjunction with a reconfigurable network topology, improves throughput by up to 2.2x compared to established routing protocols, and even comes within 10% of the throughput performance of impractical adaptive routing that has instant global congestion information.