First, let’s acknowledge that different students may benefit from slightly different actions in any given posture. So, the most accurate way to answer this question is to suggest most students will benefit from engaging their glutes in most backbends. Here’s why:
The gluteal family is composed of the gluteus maximus, gluteus medius, and gluteus minimus. When the glutes and hamstrings engage—particularly the lower fibers of the gluteal msucles near the hamstring insertion—they extend the hip-joint. This motion initiates all backbends and helps keep the pelvis and spine congruous. Gluteal engagement also helps fire the paraspinal muscles and stabilizes the sacro-illiac joint—both of which facilitate pelvic and spinal balance in backbends.
But, let’s answer the question with a little more nuance since some backbends are enhanced by gluteal engagement and others are not. Prone backbends like Locust Pose and Cobra Pose probably don’t benefit as much from gluteal contraction because the weight of the pelvis rests on the floor during these postures. This means that you don’t need gluteal strength to lift the pelvis because it’s not moving in the posture; you also don’t need the stabilization that the glutes provide because the pelvis is supported by the floor.
In kneeling backbends like Camel Pose and supine backbends like Bridge Pose and Upward Bow Pose, gluteal engagement is more helpful. These postures produce a greater degree of spinal extension so it’s even more important that the pelvis and spine move cohesively. Engaging the glutes, particularly the lower fibers of the gluteus maximus near the hamstring insertion, will help maintain this balance rotating the pelvis slightly back over the top of the legs. This will help reduce lumbar compression—the feeling of your lower-back “crunching.” Even more, the glutes help lift the weight of the pelvis in supine backbends. If you don’t use the glutes in these postures, it’s more likely that you will unnecessarily burden less efficient muscle groups.
Some teachers and students are concerned that using the glutes will make the knees splay too far apart. This is a legitimate concern, but it’s easily managed. All you have to do in this situation is co-contract the muscles that line the inside of your thighs, the adductors. Firing the adductors while you engage the glutes will keep your thighs nice and neutral.
Excerpt from YogaGlo Article Backbends: Why and When to Squeeze Your Glutes by Jason Crandell