Not Muslim sharia; it is Roman Catholic "sharia" about contraception that the US Conference of Catholic Bishops has been trying to impose on Americans of all faiths and beliefs who happen to work at a Catholic-sponsored hospital or university.
Yet the same voices ---- Fox News, various candidates for President -- that have bitterly attacked non-existent attempts by American Muslims to impose sharia on the public have not criticized this actual real-life attempt at doing so by the bishops. Indeed, many of these same voices have supported the bishops.
The bishops warned about "religious oppression" even when the Catholic Hospital Association celebrated the arrangement that the Obama Administration worked out, making sure that health insurance companies will pay for free contraception without involving the Catholic-sponsored employers who might object.
The only threat to religious freedom was the attempt by the bishops to deny religious freedom to the employees of those institutions -- both Catholic and Other -- whose religious consciences are totally at peace with the use of contraception.
Similarly, the Philadelphia Inquirer just reported (Feb 20, p. 1) that Catholic hospitals have in the last few years tied the tubes of thousands of women who after birthing a child asked for the procedure. The operation sterilizes them. No more kids. It violates Catholic religious law. Yet thousands of Catholics wanted it, and the hospitals affirmed their conscientious decision. Are the bishops playing games here? To benefit whom?
The bishops are asserting that the only "Catholic" consciences that count are those of -- surprise! -- the bishops! Not parishioners, not women, not the adults who as children were molested or raped by priests who were protected by the bishops. This world-view mirrors and strengthens the similar view in other sectors of our society:
That "the economy" is made up of huge corporations and Wall Street bankers (certainly not disemployed workers or de-housed families);
That "the military" means generals and admirals, not soldiers whose arms, legs, genitals, minds, and even souls (through post-traumatic stress) have been blown apart;
And so on.
Meanwhile, if we are seriously trying to assess the role Muslim sharia might play in American law and society, we might learn a great deal from the role of Jewish religious law. For halakha (Hebrew for "the path") is a path of Jewish law quite parallel to Muslim sharia in its place in the USA.
In the USA, each -- halakha and sharia -- applies only to those who choose to follow it.
Each is subject to varied interpretations. Indeed, since there is no central hierarchy in either Jewish or Muslim communities -- no "Pope" -- it would be a great deal harder for either community to impose sharia or halakha on the rest of the country than it is for the Roman Catholic bishops.
(But I must acknowledge that on some foreign-policy issues, the Government of the State of Israel is able to mobilize so-called "mainstream" American Jewish organizations for unanimous support in ways similar to how the Vatican can mobilize the bishops on contraception, stem-cell research, etc -- even when the grass-roots of each community disagrees.)
In almost all cases, Americans can invoke US law to enforce sharia or halakha only when two people have made a contract to live by some specified authority's interpretation of that path. In that way it is no different from any contract to accept an arbitration authority that two Americans of any sort might make with each other, and then might go to court if one party tries to break the contract.
The only case in which halakha might be said to become American law is that in about a dozen states, there is a legal provision that no one can label meat "kosher" unless it has been slaughtered according to the traditional (some laws even say "Orthodox") Jewish practice.