Why should Christians care about economics? There are a few reasons which come to mind.
First, we should care for the same reason we care about any social science, like psychology or sociology. Economics is trying to understand a few fundamental ideas about how the world which God made works. Economics can't explain everything - but no one discipline can. Not even theology can explain the whole of the human experience.
The world is too complicated to be boiled down, and life has too much texture to be understood using only one tool. But each tool does make a contribution to our overall understanding. We Christians have a responsibility as stewards of God's creation to understand the workings of the world around us, and this includes the economy.
Second, economics is more than just how money works. Too often we hear the term "economics" and we immediately begin to think about spending, or money circulation, or debt. This misunderstands the true contribution economics makes to our understanding of the world.
At the heart of economics is a concept which touches everyone's life - believers and non-believers alike. Here it is in one sentence: resources are scarce. Ultimately, we have to make choices about how resources are spent and used because we only have so much.
Thinking about how to use our scarce resources leads us to grapple with trade-offs and incentives, and wrestling with trade-offs and incentives is what economics does best. Economics is about so much more than money - it's really an investigation of how people make decisions and the subsequent impact those decision have.
We can use economics to pull apart decisions made by individual consumers as well as the choices made by firms and producers. We can use it to better understand the implications of choices the government makes. We can use it to anticipate how something might turn out, and we can use it to better recognize our blind spots. At its best, economics may even help us make better decisions going forward.
Lastly, economics helps us deal with faulty explanations for why scarcity exists or why certain decisions had certain consequences. If we Christians are as committed to truth as we like to think we are, we cannot allow ourselves to be lead astray by explanations which are false - regardless of how well those explanations align with our personal opinions.
Neat and tidy explanations are rarely both accurate and complete. Having a way to test those explanations is important for people committed to the concept of truth, especially in complex situations with lots of variables and incentives. Economics, including the way economics can teach us to think, can be just such a tool.
The field of economics has identified several principles which seem to hold more often than not. Think of things like supply and demand, how interest rates work, or identifying externalities. If I have an explanation which violates one of these principles, I'd better also have some strong evidence.
Inasmuch as economics helps us understand and navigate the world around us, it's worth the time and effort.