Civil Law systems have a doctrine similar to stare decisis with the same logic--fairness in outcomes. It just operates differently because of different views about the structure of government.
I think the main reason that Civil Law systems have voiced opposition to judge-made law is because since their advent (French Revolution onward) Continental systems have emphasized democratic control and thus the supremacy of the legislature, whereas Anglo-American law historically emphasized (or reflected) competing power structures. An early French constitution made it criminal for a judge to "invent" a rule to settle a case; if the law was ambiguous the judge was supposed to refer the case to the legislature. But guess how many times a court declared a law ambiguous and referred it to the legislature? (Point being, Civil Law systems noisily refuted the legitimacy of judge-made law, but the reality was different.)
It's notable that Parliamentary Supremacy didn't completely solidify in Britain until the late 1700s. American law didn't inherit such a notion of unlimited legislative authority. The concept of Substantive Due Process emerges from this environment, as does the far less controversial Judicial Review (from Marbury v Madison).
Also, FWIW, there's a common misconception (even among lawyers) that the Civil Law is somehow more closely related to Roman Law than the Common Law. That's not really true. Roman Law actually had judge-made law and something like stare decisis, though the technical details were quite different. Emperor Justinian attempted to impose reforms, but these were widely opposed and occurred at the tail end of the Roman Empire. In as much as the Civil Law was based on interpretations of the Justinian Code, that doesn't mean it was reflective of actual Roman Law. And in any event, most of the major distinctions between the Civil Law and Common Law emerged long after misinterpretations of Roman Law had permeated everybody's legal thinking.