Final answer:
The political compass category that sought moderate change is the Libertarian Right, which aligns with moderate economic liberalism and moderate social conservatism, indicative of the center-right ideology.
Step-by-step explanation:
The question: Which political compass category wanted moderate change? relates to understanding the nuanced political ideologies that exist beyond the simple left-right dichotomy commonly used in political discourse.
Based on the provided information, the category that represents a blend of moderate economic libertarianism and moderate social conservatism corresponds to the ideological core of the contemporary Republican Party or center-right in the United States. This combination aligns with the option which suggests moderate economic liberalism and moderate social liberalism. Hence, the political compass category that wanted moderate change and can be associated with this description is likely to be the Libertarian Right.
This category falls within a broader spectrum where the center left and center right constitute primary subgroups under the umbrella of enhancing individual rights and promoting a capitalist economy while maintaining certain social conservativism, thus aiming for a balance rather than extreme change.