You might be surprised to hear that US courts consider Sharia law in the first place. In fact, it's never happened in Kansas,
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Nationally, US courts deal with cases involving Sharia law the same way they deal with any cases involving religion. The courts apply American law, but "recognize the right of people of faith to agree to settle disputes in accordance with the principles of their religion - a right exercised routinely by non-Muslims," says a report from the ACLU.
Within the Kansas state senate, debate about the bill was highly-charged and emotional. Supporters argued passionately that it was needed to protect American rights from being overridden by foreign laws. Senators opposing the bill felt just as strongly, calling it intolerant and also unnecessary, since the bill merely reiterates something that is already the case - that US courts base decisions on US law. Since the bill has become law, a spokesman from the Council on American-Islamic Relations called the bill a "pander" to "growing Islam-phobia."
A similar law passed in Oklahoma was overturned by federal courts in 2010, because it was deemed "discriminatory."