This a simple video I put together to explain when, why and who would need to have their glutes 'relaxed' in a cobra, king cobra or up dog pose; and with bridge they are suppose to be on for the movement to be performed safely.
Activating the glutes help create the stable platform from which to move. While it is important when learning to look at each aspect of the body in segmental parts and how the parts function, this is not how the parts work together.
While necessary to consider the function of the individual parts, healing is unsuccessful without the consideration of how these parts achieve the harmonious actions.
Over the years of attending yoga classes one of the cues that bothered me the most was while in up dog, cobra, a king cobra, and especially bridge was being told to let go of the glutes b/c it would either protect the back or it was to keep the work out of the lumbar spine. This is a misunderstanding as to what role the glutes play in stabilization of the lumbar spine, pelvis, hip, knee, and ankle and the shoulder.
The glutes' role around the spine is simple: If you don't have strong glutes you are going to extend and flex at the spine instead. Strong glutes encourage good lifting and movement techniques. Stability is not only about quantity of motion and the quality of the end feel, but about control of systems which allow load to be transferred and movement to be smooth and effortless.
The thoracolumbar fascia (TLF) and its supporting musculature (glute max and lat dorsi) bridge the lumbar spine and pelvic girdle. While it plays a significant role in stabilization of the lumbar spine, it is also significant in the transference of force from the trunk to the lower extremity; the glutes play a global role in stability.
When the glute max and the contralateral lat dorsi contract this creates compression in the SIJ, compression creates stability. This compression approximates (brings closer together) the posterior aspect of the innominates ('hip' bone) and contributes to the force closure mechanism. The glutes role around the sacrum is to provide stability through an action called force closure.