In the military, if the enemy forces you to renounce the United States, it is not treason. Treason requires intent to commit treason. If a terrorist tortures you to get you to bow to their god, and you do, without the worshiping, are you sinning? Does not God know what is in your heart? What if the terrorist physically forces you into a bowing position, is that bowing to another god?
Some martial arts use all kinds of gestures and movements in combination with, or instead of, bowing. Does performing their ritual movements constitute bowing in worship of another God? Is a military person who salutes, the flag of country that rejects our Christian God, sinning before God? If a citizen salutes the United States flag, is he or she worshiping America? Some say we have become a godless country. Does this mean that when you say the Pledge of Allegiance you are pledging your allegiance to a country that rejects God! Remember what happened to the people of Sodom and Gomorrah, just living in godless cities got them killed.
When you go to a school, college, or professional football game and cheer, recite the team motto, hold up the school sign, or dress in the school colors, are you bowing to, or worshiping, the school or team? The difference between what is respect and what is worship is in the eye of the beholder.
Most everything is subject to interpretation, the Bible included. That is why there are so many opposing religions that each bases its beliefs on the same Bible and thinks that its interpretation of the Bible is the correct one. I once had an investigator who working for me who was fundamentalist Christian. In a conversation, he mentioned that, since the Bible does not mention using a piano or organ in the worship of God, his church does not use them. I asked hum, “Why does your church use air conditioning to cool the church, church telephones to call sinners, or a church bus if they are not mentioned in the Bible?” I received no answer; he just walked away.