This is not flame throwing...
It is a honest question. Do you think a Christian would bow to a Muslim King?
I know I wouldn’t. There is only one King I would bow down to.
I would be respectful but not bow.
I would never slip and say I was a Muslim either.
It occurs to me this may be one reason why it might be so. Muslims are ostracized and killed for such confessions. As far as I know, a Muslim doesn't confess Jesus as Lord unless he has actually been converted. In fact, the Bible says no one can call Jesus Lord but by the Holy Spirit.
In Official US State Department Diplomatic Protocol:
An American does not bow or curtsy to anyone.
Bowing down to a foreign monarch or potentate is a violation of this rule.
The only exception is made for Roman Carholics, who may bow down to the Pope, and kiss his ring.