What constitutes "freedom of religion" is a question subject to disagreement. Some would feel that it infringes their religion to make it a crime to kill infidels who refuse to accept what the followers of a particular religion "know" to be true about God. Some would feel it infringes their religion to disallow use and possession of marijuana and cocaine, or to punish drunk driving that did not actually hurt someone. Some would feel it infringes their religion to disallow a person from having multiple wives, or from marrying and having sex with children. Yet, the courts have allowed the government to prosecute all those actions, whether the individual asserts religious rights or not.
The United States does not rule the whole world, and has only limited ability to influence the actions of other nations, especially theocracies that are most hostile to our democratic institutions. The President and Congress decide what relations our nation will have with other nations. So, it is constitutional for the US to have an ambassador in Saudi Arabia, and constitutional for the US not to have an ambassador in Syria, even though either government could arguably be labeled a theocracy. No matter what the US does in foreign policy, you continue to have the right to maintain your religious beliefs. When you move from beliefs into action, the courts have made limits on those actions, otherwise, every person would constitute his own government, with the ability to steal, or to burn unbelievers, or to rape children, upon declaring a religious principle.
The First Amendment also protects freedom of speech, but that does not mean I can walk up to you and say "Give me all your money or I will shoot you," an act that would consist entirely of speaking words.
Contact me at 248-399-6930 for a free consultation. You and I do not have an attorney-client relationship formed by our communications on this website. Advice given by me on this website is general advice based on partial information. You should not rely on any advice given without first hiring a lawyer in the area where the case is pending, and providing that lawyer with full information.
The "Establishment Clause" of the 1st Amendment applies only to congressional acts, and via the 14th Amendment, to the actions of states as well. Simply because you may describe another country as "heavily theocratic" does not mean that any action taken in regard to that country is done so in regard to the nature of its governance. Nor would even an action based expressly on the theocratic nature of that country automatically implicate the Establishment Clause. Moreover, American courts historically avoid taking cases that encroach on the development or implementatoin of foreign policy.