Sharia literally means "law" in Arabic (although it generally has an implied religious connotation these days). Like you said that much like our legal system, there is a fair amount of debate and variation among sharia scholars. Just like different American constitutional experts have opposed and supported things like slavery, different sharia scholars have opposing views on almost every issue.

Groups like Al Qaeda, ISIL and the Saudi monarchy for that matter have invested a lot of effort in propagating a very reactionary, brutal interpretation of Sharia. Even though this view is largely opposed by mainstream institutions like Al Azhar (not to mention most regular muslims) the slave-taking, woman-stoning, beheading interpretation of Sharia is the most visible version of Sharia in the modern world, even if it's not completely representative. This combined with complicated anti-muslim sentiments across the west has led to anti-Sharia movements.