Because this case was decided by the highest court in the land, it sets a precedent for future cases that can only be overturned by the Supreme Court itself. Even the Supreme Court is unlikely to overturn its precedent, however, unless its composition changes significantly.
In the future, then, this case establishes a rule that the immigrant bears the burden of proving that the crime they were convicted of does not constitute a crime of moral turpitude. In many cases, especially with state law charges, this is likely to prove an impossible task.
The Court’s decision, however, can be effectively reversed without waiting for the Supreme Court to overturn its own precedent. Since the decision was based on the Supreme Court’s interpretation of a federal statute (the Immigration and Nationality Act), Congress can evade Pereida v. Wilkinson by simply changing the wording of the statute.
Until then, immigrants with criminal records are going to face a much more difficult time obtaining the cancellation of removal.