You seem to be saying that the existence of economics as an academic discipline implies that economics theory must be based on (pseudo-)mathematical models. I

You seem to be saying that the existence of economics as an academic discipline implies that economics theory must be based on (pseudo-)mathematical models. I don't know in the US but in France we have two families of economists in academia: orthodox and heterodox. The orthodox family is the one of the economists who thinks that their field is a hard science with laws comparable to that of physics. It is the mainstream family. It may be further simplification of the reality but I think almost all of them of them could be considered rightists politically. Sadly, they are currently taking over the entire field by making it very hard to get an academic position in economics if you are not on their team. Heterodox economists are the ones who believe their field is more like a social science. They have a variety of point of views depending on their approach (sociological, anthropological, historical, philosophical, etc.). They are often categorized as more leftists relatively to orthodox (again, I may be oversimplifying here). Many of them are "refugees" in other academic field such as sociology (e.g., Frédéric Lordon or Bernard Friot). Anyway, my point is that economics could very well be an academic discipline without being a religion. EDIT: the Austrian School of Economics that fiatjaf mentions in another comment is an example of what is called heterodox economics.