Almost every English-language argument about sharia, for and against, is conducted without the distinction that Islamic scholarship considers elementary.
Sharia is the divinely given way. Fiqh is the accumulated human effort to work out what it requires. The first is held to be perfect and unchanging. The second is the product of named jurists reasoning from texts, and Muslim scholarship has always held it to be fallible, revisable and plural, because it is human work.
What gets called "sharia law" in English is almost always fiqh, and frequently it is one school's fiqh, or a modern state's statute claiming descent from it.
The plurality is the system
Sunni Islam has four surviving schools, each named for an early jurist, each dominant in particular regions, and each regarding the others as legitimate. Twelver Shia jurisprudence differs again in its sources and admits reason in a way the Sunni schools do not. Ibadis and Zaydis have their own.
They disagree, and the disagreement is not a scandal to be resolved. A body of law in which four incompatible answers are all orthodox is not operating like a statute book.
Most of it is not about crime
The jurists classify every human act on a five-point scale from obligatory to forbidden, and the overwhelming bulk of the classical manuals concerns worship, purity, marriage, inheritance, contract and diet. The fixed scriptural punishments that dominate Western coverage occupy a small part of the material and were hedged with evidentiary requirements so demanding that classical jurists made conviction close to impossible.
What the modern state changed
This is the part most often missed, and it cuts against polemics in both directions.
A classical jurist issued an opinion. It bound nobody by force; its authority was scholarly, and a questioner could go to another jurist. Modern codification, beginning with the Ottoman civil code of the 1870s and continuing through twentieth-century national legal systems, converted that into enacted statute, with one answer, applied by state courts, backed by police.
That is a transformation, not an application. Some of the sharpest criticism of state-enforced sharia comes from Muslim scholars arguing exactly this: that a law imposed by coercive state machinery has stopped being the thing the jurists were doing, whatever it is called.