I'm writing this post for my 'faith' friends who are questioning the compatibility of yoga with the Christian faith. This is a real issue for some. It was an issue for me several years ago. But I want to offer a few reasons as to why there is compatibility between these two traditions.
First, Christianity borrows from culture. There's no such thing as 'pure' Christianity. All religions, including Christianity, have borrowed from the cultures in which they have grown up in. Christianity grew up out of Judaism to state the obvious, then borrowed from Greek neoplatonic philosophy after it had used the infrastructure of the Roman Empire to promulgate its message. It has also adopted or rather co-opted pagan festivals (Christmas being a prime example), used another world empire to further its influence (British this time), engaged with Enlightenment thinking (the prioritising of the intellect) and even 'rock music' (once seen as 'satanic') to create modern worship music. So in short, Christianity has appropriated useful vehicles within existing cultures to propagate its own ends. Yoga as exercise is a modern 'vehicle' worth exploring in my opinion.
Second, the body is neutral. Yoga in the West, which is the yoga I've discovered and use (Modern Postural Yoga to be more precise) is an amalgam of postures, some that originated hundreds of years ago but many more recently resulting from engagement with Swedish gymnastics, calisthenics, body building and other modern exercise forms. Sometimes it's hard to tell what is a yoga posture, a pilates posture or what is simply a stretch. The body is a neutral vehicle that we can move in any number of ways and that doesn't mean that we are buying in to a whole Eastern philosophy (if we'd rather not). Let's just remember that we can use money, sex and authority for good or bad, it is not the thing itself that 'corrupts' but rather how we use the thing.
Third, therefore, is the intention behind the use of yoga postures. You can choose whether the goal is to get a beautiful body or find a way to destress; we can worship a Hindu deity if we want, or we can connect to our own god (including the Christian God) through mindfully using yoga postures. We all bring intention to neutral things: food, sex, money, power, the words we speak and the postures we engage in. As St.Paul said nothing is 'unclean' in and of itself, (only if a person regards something as being 'unclean' then it is for that person). So my advice is: be like Paul. Set your intention in accordance with your faith, know that the body and postures are neutral and that yoga exercise can be a borrowed vehicle to live more fully in body, mind and soul.