The sun salutation proves it so, it is not defined by Hinduism and there fore Yoga is not defined by any religion. Just because Yoga came from India which is mostly Hindu, does not mean that it is related to any religion, and is based on Hinduism when it is not.
Yoga has strong roots in Patanjali and that is not Hindu text. Mantra can have religious context, and that can include prayer and that can be included in your practice.
There is power in a prayer to the sun, for we are the power of it.
Yogis who came to this information wanted the people to have this technology.
Yoga never defines what religion to practice. But if it did i think Yoga would say practice your religion.