I think that the similarity between them is that Both work to limit aspects of their causes.
Political conservatism is a political and social philosophy that seeks to preserve a range of institutions such as monarchy, religion, parliamentary government and property rights with the aim of emphasize social stability and continuity.
While energy conservation is an effort made to reduce the consumption of energy. This can be achieved by consuming less energy or using energy more efficiently.
We could say that both want to return the way things were before and in order to achieve this limit some aspects of their respective causes.
I hope this answer helps you.
