Brief history of yoga
Yoga began as a Hindu practice, around 10,000 years ago. I found a brief article that concisely explains the history of yoga:
Separating the stretches and exercises from the religious aspect
Yes, this is possible.
As a Christian, I have been taught by various people, for years, that Christianity and Yoga are incompatible. While I understand that thinking, a Christian should not get involved with the spiritual side of Yoga, only the exercises, and these are not incompatible with Christianity, any more than any other type of exercise.