The 1st Amendment cannot be diminished without a Declaration of War. However, make all immigrants to accept in statement and writing that shari'a is inferior to American law. That we can do.
What would be the point of that? That's the case already in U.S., whether they sign such a document or not.
The overwhelming Muslims in the U.S. who appeal to Sharia Law and Imams do so mainly to resolve domestic matters for which there is no requirement for them to invoke U.S. common law means of redress. In matters like spousal abuse, which may (seem to) fall into a "murky" area if the abused person doesn't opt to (for whatever reason) seek secular redress, if a police officer or other individual gets wind of its having possibly occurred, s/he can, absent the abused person's consent, bring the matter into the U.S. justice system as needed, at which point Sharia Law instantly becomes subordinate to U.S. secular laws.
Since you mentioned Sharia Law, I suspect you're familiar with the various conservative opinion outlets that have over the past year or so referred to the responses obtained in a couple
polls taken by the Center for Security Policy, itself another promulgator of opinion. For now, I'll just suggest you look objectively, as someone who wants to obtain complete and contextually relevant information, at what the questions in the CSP polls ask and what they don't ask. Then examine what inferences and assertions are (have been) made in the conservative opinion press follow from the questions asked, but that also present the answers in the context that non-Muslim would understand, and without also noting the context in which a Muslim would perceive the question.
A Hypothetical Example of What I Mean:
Suppose Christians were polled and one of the questions is "Are Jesus' commandments superior to secular law?" Assuming 51% or more of Christians surveyed answered yes, some political group with an axe to grind would surely assert something like "most Christians think Biblical law should supercede the Constitution."
Yet having been a Christian for a long time, were I asked that question, I would impose my own contextual relevance to the question. One possible context is that I think Jesus' law to "love one's neighbor as oneself" is more important than anything in the Constitution. Another context I might apply is that I see the law "thou shall not murder's" having been given in the Bible superior to the fact that the U.S. code of laws contains the same prohibition.
An reader of an opinion piece who doesn't well understand Christianity and how it is applied by my "flavor" of Christian belief would all but certainly have no idea of either of those contextual reads to the question that I applied. It is that same stance of ignorance that most Western non-Muslims are necessarily in when it comes to evaluating the precious few questions in the CSP surveys. I was certainly in exactly that position earlier this year when I became happened upon some of what I was hearing/reading from conservatives about what U.S. Muslims think re: Sharia Law and its application.
It took me quite a lot of reading to arrive at a place whereby I have a sense of how a Muslim may have construed the questions the CSP asked, but when I had finished my research, I saw that how they likely viewed the inquires and how I viewed them were very, very different. What I'm saying is that one must, if one considers oneself equitable and intellectually rigorous, some legitimately critical research and analysis needs to happen before one even considers putting stock in the results of the CSP's surveys about what Muslims think about Sharia Law.
What the CSP says the responses mean and what undoubtedly most U.S. Muslims would say they had in mind when answering the questions aren't in fact the same things. That sort of discrepancy isn't uncommon in polls issued by groups that have a political "axe to grind."