The question is do executive orders have to be obeyed? I say no illegal order has to be obeyed. At least by me anyway.
The answer is "Yes" but it applies only to federal employees of the executive branch of the government. Of course executive orders must be legal and must not contradict either the constitution or the laws. The president is the nations highest law enforcement officer. He is sworn to protect and defend the constitution. That is why we are said to be led as a nation of laws, not of men.
The president is not the king of America, no matter what he thinks. He is more like a CEO of the Executive Branch of the government. He has no right to order the states using an executive order.