I'm no lawyer, but we allow plenty of international law to be considered in this country. Many of our global companies will sign contracts that specify that the contract will be adjudicated in a foreign court. So for instance, if a US company is doing business in France, it might agree to settle any disputes in the French courts. If it then tries to sue it's French partner in a New York court, the New York court should require it to use French courts. If we didn't allow that, then it would put a serious damper on our economy. One of the keys to getting foreign investment is to have a strong and stable set of laws and regulations that have a (somewhat) objective way of dealing with international law. And obviously there are plenty of US companies doing business in Middle Eastern countries.
And the thought that all muslims believe in Sharia law is more fear mongering. Sharia law is not the rule in all Middle Eastern countries and many muslims dislike it. In Egypt, for instance, people will commonly tell you that both men and women are supposed to dress modestly. Many women wear tight sexy clothing and don't wear anything covering their hair. Doing business in the middle east in the nineties, I only saw burkas on the Saudi women and in the desert. When in Rome, do as the Romans. I wore knee length skirts (all my suits were knee length anyway) and cap sleeves instead of sleeveless shirts. I could have dressed however I wanted, but it would have been impolite and impolitic.
I found Egyptians to be as nice as Midwesterners, maybe even nicer if that's possible. I've met many a loving, family oriented, kind hearted muslim. Sure there are some wacky ones, but we have those too. People are people. I'll never forget the saudi woman on a street corner. She had the whole black getup on, including a facemask! I was surrepticiously checking out her garb, but I didn't want to be rude and stare so I looked away when she looked at me. Suddenly, I realized she was checking out my garb, and trying not to be rude. We both smiled sheepishly at each other from across the street. Both feeling and doing the same thing even though we were from vastly different cultures, geographies, ethnicities, religions, etc. People are people.