Okay, so here is my totally unscientific take on why the right-wingers hate, or at least, don't like or trust the American legal system. This is certainly not a recent development, as anyone who was alive in the 1960s and can recall reading about "Impeach Earl Warren" bilboards put up by the John Birch Society. Nor, is it just limited to the right's dislike for rulings in criminal cases, although those do seem to really get right-wingers foaming. It more about holding power accountable and the courts being used by those without power against those with power.
First of all, a lot of developments in the United States that the right is upset with resulting from decisions of the United States Supreme Court, and the Federal courts in general.
Starting with the civil rights cases that started coming up in the 1940s and then the Brown v. Topeka decision, the United States Supreme Court was the only Federal institution that was responding to the legitimate demands of the nation's African-American community for civil rights. The Congress was dominated by white Southerners, who could kill civil rights legislation on the Hill, especially in the Senate. But, the South couldn't control the U.S. Supreme Court. This meant that the justice system became the primary vehicle to challenge racial inequality until the period of 1964-1965. This obviously engendered a lot of hostility toward the Federal courts.
Not only did you have the Supreme Court blazing new paths on civil rights, but you also had the "one man, one vote" decisions of the early 1960s, which ended rural domination of state legislatures.
That was followed by Supreme Court decisions that incorporated selected parts of the Bill of Rights into the 14th Amendment's Due Process Clause. This meant that state criminal prosecutions could be challenged in Federal Courts, which undercut both the power of prosecutors and state court judges.
Then we had the Griswold which began to establish the right to privacy in the 14th Amendment Due Process Clause, which led to the Roe v. Wade decision and all the decisions involving abortion since the Roe decision.
So, from the view of right-wingers, the American legal system, and particularly the United States Supreme Court, has been a source of frustration.
But I think that it goes much deeper than the particular details of a particular decision or line of decisions. What all the above decisions had in common was that they allowed people who didn't have power to challenge those with power. They allowed people who didn't have the political power to get results that a conservative dominated poltical system didn't want them to get.
There is a deep streak of authoritarianism that runs through the right. They love authority, they like bowing down to authority, and they want authority in their lives. (Assuming, of course, that the authority is exercised by people like them, and not people like Barack Obama.)
A legal system that respects the rights of everyone who comes in front of it, that allows the powerless to challenge the powerful, and that holds the powerful accountable is a threat to authority and to those that adore authority.
This trait is why they favor corporations over consumers, government officials over the governed, and the executive over both the legislative and the judicial branches. It is why they are coming unglued over Holder's decision to try detainees in Federal courts.
It is why they will criticize the legal system and try to make sure that the courthouse doors are closed to those without power while swinging wide open to those with power.