Hello Dan,
You are correct about the reference towards eating food dedicated to idols. However, there is a part that I wanted everyone in this this thread to realize. Paul said "If meat causes my brother to offend, I will eat no meat while the world stands." I know a lot of Christians who are content with doing the bare minimum and/or not giving everything up for the sake of Jesus Christ because many Christians still heavily lust after comfort at the expense of serving God and their fellow man.
I would not do yoga at all simply for the fact that it does have modern pagan ties and that has a high probability of causing somebody to stumble. Also because personally knowing that it does have pagan ties might cause me to stumble as well. Paul said eat what is given to you but if someone says "This food was offered to idols" then refuse it for conscience sake. Most folks know that yoga is indeed offered to idols. It is up to the discretion of the person if they ever to choose to do it but keep in mind that there are always people watching you and observing your behavior as a Christian. There are 5 Gospels and most people will only read the very last one: Matthew, Mark, Luke, John, and the Christian. Be careful how your story is written.
If someone incorporates yoga moves into stretching before military PT, I'm not going to sit in the corner and refuse to do them (unless they start doing all the Eastern religious mouth sounds and such with it). However, i'm not going to walk into a yoga lesson, even if I don't see any baby Christians around no more than I would go to the local club and have a glass of wine if there are no Christians or seekers around to my knowledge. Even though I may have every good intention, it could still end up hurting someone whether I perceive it or not.