Should a Christian do yoga?
Your question has complexities because yoga is viewed in two different ways.
Yoga originated in India and was strongly connected to Hinduism. It was later picked up by Buddhism and Jainism. The goal of yoga as a religious practice is for the practitioner to attain a state of perfect spiritual insight and tranquility.
"The eight steps of Classical Yoga are 1) yama, meaning “restraint” — refraining from violence, lying, stealing, casual sex, and hoarding; 2) niyama, meaning “observance” — purity, contentment, tolerance, study, and remembrance; 3) asana, physical exercises; 4) pranayama, breathing techniques; 5) pratyahara, preparation for meditation, described as “withdrawal of the mind from the senses”; 6) dharana, concentration, being able to hold the mind on one object for a specified time; 7) dhyana, meditation, the ability to focus on one thing (or nothing) indefinitely; 8) samadhi, absorption, or realization of the essential nature of the self. Modern Western Yoga classes generally focus on the 3rd, 4th, and 5th steps" ["General Yoga Information," American Yoga Association].
Repeatedly I find people stating that yoga is not a religion, but notice that classical yoga teaches a moral system (steps 1 and 2) and contains features of Hinduism. Oddly, the very emphasis that it can be acceptable to all religions is a feature of Hinduism. "All religions are true, we are told, but Hinduism condenses them all by preserving such of their characteristics as may be acceptable to all" [Louis Renou, The Great Religions of the World, p. 51]. In Hinduism, "Prayer consists of the silent recitation of sacred formulae (mantra) which are repeated indefinitely. ... This type of prayer is an aid to mental concentration and is thought to bring about the desired effects of protection, the fulfillment of a promise or expiatory virtue ... Strengthened by Yoga exercises, meditation can lead to such a paroxysm of tension that the exercitant can accomplish the ultimate aim proposed in all Indian religious thought: a state of union with the Absolute" [Louis Renou, The Great Religions of the World, p. 32-33]. In other words, a Hindu's idea of prayer is to empty one's mind of all thought so that connection with the universe is obtained. (See steps 5, 6, and 7 above.) In Hinduism, deity is a vague concept of power that supposedly resides in all things, making all things a part of this deity. The ultimate goal for a Hindu is to realize that he is a part of God and is God. " “The impersonal God is that Being which dwells in the heart of everyone. Every individual in his true nature is the Impersonal God. That is why the Vedic philosophy of the Upanishads declares: ‘I am That, Thou art That, and all this is That.’” [Transcendental Meditation, p. 269]. If you will notice this is what step 8 listed above is about.
But in the United States and other western cultures, yoga is often stripped of its religious ideas and is practiced solely as a set of exercises that emphasizes flexibility, strength, balance, and controlled breathing (i.e. steps 3 and 4 listed above). If it is kept merely to that level, I see no problems with it. My main qualm is that many teachers of yoga, even while denying that what they are teaching has religious meaning, do in fact teach portions of Hinduism without recognizing it.
Another worrisome aspect of yoga is the long lists of ailments that yoga is supposed to be able to cure. Such over-exuberant claims of benefits smack of the old snake-oil salesman.
"But have nothing to do with worldly fables fit only for old women. On the other hand, discipline yourself for the purpose of godliness; for bodily discipline is only of little profit, but godliness is profitable for all things, since it holds promise for the present life and also for the life to come" (I Timothy 4:7-8).
We know exercise benefits the body and yoga includes exercise, but don't allow yourself to accept the religious aspects of yoga. I know of many workouts that include yoga positions, but that is as far as it should be taken.