Now, if you want my personal view on this matter. I think a Christian should do Yoga, because it is not debatable that Yoga is very good for improving ones health. This is the scientific consensus on Yoga based on decades of scientific studies. However, they should not start drawing arbitrary distinctions that they are only going to do asanas and not pranayama and meditation, because while asanas have obviously immense benefit for ones physical health in keeping the body supple, flexible, toned and healthy, the latter has immense benefit for ones mental health in keeping the mind focussed, patient, tolerant, positive and strong. This too is backed up by the scientific consensus and decades of scientific studies.
A Christian should therefore have no problem doing all of Yoga and indeed be a Yogi, as clearly the benefits of Yoga and what it does for you are facts. A Christian has no choice but to accept facts. Just as he must accept the heliocentric model, evolution, big bang, atoms and other facts of science. Like he has with science, he must also learn to accomodate Yoga with their beliefs.
There is no compulsion in Yoga for the yogi to accept any doctrine which is not their own experience and reason. Most gurus will not ask you to accept atman, brahman, reincarnation, kundalini, prana and chakras. However, they will certainly teach these things, because they are the theory Yoga is based on. The Christian will have to simply take what they want and reject what they don’t want, but they cannot expect Yoga to be taught without them. Therefore the Christian is going to have to accomodate Yoga and not the other way around.
Yogiadam, an atheist, is already doing this. He takes what fits his own experience and reason and rejects what doesn’t. One of the forms of Yoga he is practicing, Satyananda Yoga, is one of the most serious and religious forms of Yoga. Yet he survives. So there is no reason a Christian cannot do the same.
Yoga itself will not contradict a Christians belief. However, the spiritual results it can produce, will contradict their beliefs. As I have said many times before as soon as ones practice is mature they will experience things like out of body experiences, astral projections, psychic phenomenonon, kundalini awakenings, past life memory recall, mystical experiences. As and when this take places, the Christian will be forced to accept many of the doctrines of Hinduism, because they will not be to deny their own experience. Eventually they will completely accept Hinduism.
A real yoga guru will never force a Christian to chant mantras they are uncomfortable with, or read scriptures that are outside their religion, or pray to deities that they do not believe in or meditate on something against their faith. Rather they will advise the Christian to chant mantras that are either secular(peace, love, freedom etc) Read their own bible and Christian scripptures, and pray to their own deity and meditate on what is in their own faith. This is because Yoga is process-specific, not object-specific. You can assume as your object anything that will aid your practice.
A Hindu will obviously get more out of Yoga than a Christian. As they can chant mantras in the language of Sanskrit, which was designed especially for mantras and the sounds have very powerful effects on the psyche. They have a much wider selection of scriptures to read which are all yoga-specific(Gita, Yogasutras, Vedas, Upanishads, tantras) And they have dozens of colourful deities to choose from, each one with a vast tradition of symbols, stories, artwork and temples. However, none of this is mandatory to be a yogi. It is simply very helpful. As Yoga is a Hindu tradition, the Christian should not be surprised to be exposed to Hindu imagery. Again, it is their choice on how much they want to partake of the Hindu imagery.
Fortunately, there are many liberal Christians like Pandara who have no problem in partaking in the Hindu imagery. They simply add it to their Chrisitian imagery and adapt it.
I know of many pastors who have incorporated Hindu imagery into their preachings. It is a sign of maturity to be able to partake of other religions. I myself partake of Christian imagery in that I sing gospel, recite the lords prayer and cite from biblical scripture. I also partake of Islamic imagery. Native American. Pagan.