In science you develop a hypothesis to explain the cause of an observed outcome. You then develop a laboratory test to see whether that hypothesis holds true under varying conditions. If the hypothesis fails the test, it is abandoned. If the hypothesis is validated, mathematical formulas are then developed to explain the hypothesis and to predict future outcomes.
In religion a hypothesis is presented as being fact without any credible test to validate its accuracy.
In economics, there is no laboratory testing of hypotheses and no mathematical formulas predicting future outcomes. Economics therefore qualifies as a religion. Do you agree?
The question is interesting, provocative, and borderline polemical. Economics is not pure science. In physical science, lab experiments have repeatability and reproducibility. A sincere modern-day scientist can replicate the lab results of an experiment conducted fifty years ago. One cannot say the same for any social sciences, especially economics. Say a policy that had considerable success in the 1970s United States may fail when applied to a Latin American country in 2010 as both people and times have changed (if interested, one can google "Lucas critique"). Having said that, one has to look at economists' challenging tasks. In physics, the properties of a particular particle are preserved universally. In economics, one has to deal with human behavior, which is highly diverse.
Any credible economic theory or model had to pass the test of time, which applies even to sophisticated and complex mathematical models. The everyday jargon that we hear on business news, like changes in fiscal policy, tax cuts, and feds cutting interest rates, do not come out of thin air but are based on a solid understanding of the system intertwined with historical precedents (e.g., great depression, post WW2 baby boom, 2008 global meltdown) and heavy data-driven analysis (which goes far beyond calculating simple mean and standard deviations).
Econometric techniques (think of marrying statistics with economics) that are used in forecasting all sorts of stuff (exchange rates, stocks) do not only have a strong scientific base in formulating them but also pass through large historical datasets. However, one must accept that these mathematical tools' success depends on the operator's skill and integrity. Often other social science branches complain that economics has become too mathematical. To specifically answer the last line of your question about mathematical economics, one can think of a nuanced Black-Scholes model for the dynamic financial markets. I will not answer the part related to religion directly, as these days, any comment related to religion or faith is highly sensitive. But I guess that I have answered the question broadly.